## 36018

36018^{2} = (2^{2} + 5)(71^{2} + 5)(169^{2} + 5) = (8^{2} + 5)(61^{2} + 5)(71^{2} + 5) = (13^{2} + 5)(16^{2} + 5)(169^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 36024

36024^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36025

36025^{2} = 1411^{2} + 1413^{2} + 1415^{2} + 1417^{2} + ... + 2195^{2}.

by Yoshio Mimura, Kobe, Japan

## 36026

36026^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36036

36036^{2} = 336*337*338 + 338*339*340 + 340*341*342 + 342*343*344 + ... + 388*389*390.

by Yoshio Mimura, Kobe, Japan

## 36040

36040^{2}± 5 are primes.

36040^{2} = (1^{2} + 4)(4^{2} + 4)(7^{2} + 4)(8^{2} + 4)(60^{2} + 4).

by Yoshio Mimura, Kobe, Japan

## 36046

36046^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36066

36066^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36098

36098^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36100

36100 =190^{2}, with 36 = 6^{2} and 100 = 10^{2}.

by Yoshio Mimura, Kobe, Japan

## 36108

36108^{2} = (2^{2} + 8)(3^{2} + 8)(13^{2} + 8)(190^{2} + 8) = (3^{2} + 8)(13^{2} + 8)(14^{2} + 8)(46^{2} + 8)

= (3^{2} + 8)(46^{2} + 8)(190^{2} + 8) = (13^{2} + 8)(14^{2} + 8)(190^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 36124

36124^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36132

36132^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36134

36134^{2} = 307 x 308 + 309 x 310 + 311 x 312 + 313 x 314 + ... + 1987 x 1988.

by Yoshio Mimura, Kobe, Japan

## 36156

36156^{2} = 773^{2} + 774^{2} + 775^{2} + ... + 1636^{2}.

by Yoshio Mimura, Kobe, Japan

## 36162

36162^{2} = (2^{2} + 5)(3^{2} + 5)(4^{2} + 5)(703^{2} + 5) = (2^{2} + 5)(17^{2} + 5)(703^{2} + 5)

= (3^{2} + 5)(6^{2} + 5)(17^{2} + 5)(88^{2} + 5) = (3^{2} + 5)(6^{2} + 5)(32^{2} + 5)(47^{2} + 5)

= (4^{2} + 5)(11^{2} + 5)(703^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 36213

36213^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 36279

36279^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 36288

36288^{2} = (2^{2} - 1)(3^{2} - 1)(8^{2} - 1)(17^{2} - 1)(55^{2} - 1) = (5^{2} - 1)(8^{2} - 1)(17^{2} - 1)(55^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36309

36309^{2} = (4^{2} + 3)(6^{2} + 3)(12^{2} + 3)(110^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 36312

36312^{2} = (3^{2} + 8)(20^{2} + 8)(436^{2} + 8) = (9^{2} + 8)(48^{2} + 8)(80^{2} + 8).

by Yoshio Mimura, Kobe, Japan

## 36320

36320^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36334

36334^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36344

36344^{2} = 1250 x 1251 + 1252 x 1253 + 1254 x 1255 + 1256 x 1257 + ... + 2144 x 2145.

by Yoshio Mimura, Kobe, Japan

## 36361

36361^{2} = 1322122321, a square with 3 kinds of digits 1,2,3.

by Yoshio Mimura, Kobe, Japan

## 36365

36365^{2} =1322413225.

by Yoshio Mimura, Kobe, Japan

## 36366

36366^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36372

A cubic polynomial:

(X + 7^{2})(X + 108^{2})(X + 336^{2}) = X^{3} + 353^{2}X^{2} + 36372^{2}X + 254016^{2}.

by Yoshio Mimura, Kobe, Japan

## 36376

36376^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36416

36416^{2} = (1^{2} + 7)(12875^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 36432

36432^{2} = (2^{2} - 1)(10^{2} - 1)(45^{2} - 1)(47^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36456

36456^{2} = (1^{2} + 3)(2^{2} + 3)(11^{2} + 3)(12^{2} + 3)(51^{2} + 3) = (1^{2} + 3)(2^{2} + 3)(51^{2} + 3)(135^{2} + 3)

= (1^{2} + 3)(3^{2} + 3)(5^{2} + 3)(12^{2} + 3)(82^{2} + 3) = (1^{2} + 3)(11^{2} + 3)(12^{2} + 3)(135^{2} + 3)

= (2^{2} + 3)(3^{2} + 3)(5^{2} + 3)(9^{2} + 3)(82^{2} + 3) = (2^{2} + 3)(9^{2} + 3)(11^{2} + 3)(135^{2} + 3)

= (5^{2} + 3)(11^{2} + 3)(12^{2} + 3)(51^{2} + 3) = (5^{2} + 3)(51^{2} + 3)(135^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 36464

36464^{2} = (5^{2} + 7)(6^{2} + 7)(983^{2} + 7) = (37^{2} + 7)(983^{2} + 7).

by Yoshio Mimura, Kobe, Japan

## 36480

36480^{2} = (2^{2} - 1)(3^{2} - 1)(39^{2} - 1)(191^{2} - 1) = (3^{2} - 1)(9^{2} - 1)(37^{2} - 1)(39^{2} - 1)

= (5^{2} - 1)(39^{2} - 1)(191^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36481

36481 = 191^{2}, a zigzag square with different digits.

by Yoshio Mimura, Kobe, Japan

## 36490

36490^{2}± 3 are primes.

36490^{2} = (4^{2} + 9)(13^{2} + 9)(547^{2} + 9) = (13^{2} + 9)(14^{2} + 9)(191^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 36504

195^{2} + 36504 = 273^{2}, 195^{2} - 36504 = 39^{2}.

by Yoshio Mimura, Kobe, Japan

## 36540

36540^{2} = (1^{2} + 5)(3^{2} + 5)(5^{2} + 5)(10^{2} + 5)(71^{2} + 5) = (1^{2} + 5)(3^{2} + 5)(5^{2} + 5)(16^{2} + 5)(45^{2} + 5)

= (1^{2} + 5)(4^{2} + 5)(5^{2} + 5)(13^{2} + 5)(45^{2} + 5) = (1^{2} + 5)(13^{2} + 5)(25^{2} + 5)(45^{2} + 5)

= (2^{2} + 5)(3^{2} + 5)(5^{2} + 5)(13^{2} + 5)(45^{2} + 5) = (3^{2} + 5)(5^{2} + 5)(25^{2} + 5)(71^{2} + 5)

= (4^{2} - 1)(6^{2} - 1)(28^{2} - 1)(57^{2} - 1) = (5^{2} + 5)(11^{2} + 5)(13^{2} + 5)(45^{2} + 5)

= (9^{2} - 1)(28^{2} - 1)(146^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36556

36556^{2} = (4^{2} + 3)(7^{2} + 3)(1163^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 36582

36582^{2} = (6^{2} + 3)(8^{2} + 3)(12^{2} + 3)(59^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 36624

36624^{2} = (1^{2} + 3)(3^{2} + 3)(5^{2} + 3)(999^{2} + 3).

by Yoshio Mimura, Kobe, Japan

## 36651

36651^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 36667

36667^{2} = 1344468889, a square with non-decreasing sequences of digits.

by Yoshio Mimura, Kobe, Japan

## 36720

36720^{2} = (2^{2} - 1)(5^{2} - 1)(16^{2} - 1)(271^{2} - 1) = (4^{2} - 1)(16^{2} - 1)(17^{2} - 1)(35^{2} - 1)

= (4^{2} - 1)(35^{2} - 1)(271^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36729

36729^{2} = 265^{3} + 266^{3} + 267^{3} + ... + 318^{3}.

by Yoshio Mimura, Kobe, Japan

## 36740

36740^{2} = 342 x 343 + 344 x 345 + 346 x 347 + 348 x 349 + ... + 2010 x 2011.

by Yoshio Mimura, Kobe, Japan

## 36750

36750^{2} = (1^{2} + 6)(2^{2} + 6)(12^{2} + 6)(13^{2} + 6)(27^{2} + 6) = (1^{2} + 6)(2^{2} + 6)(27^{2} + 6)(162^{2} + 6)

= (1^{2} + 6)(3^{2} + 6)(12^{2} + 6)(13^{2} + 6)(22^{2} + 6) = (1^{2} + 6)(3^{2} + 6)(22^{2} + 6)(162^{2} + 6)

= (1^{2} + 6)(6^{2} + 6)(13^{2} + 6)(162^{2} + 6) = (2^{2} + 6)(3^{2} + 6)(6^{2} + 6)(463^{2} + 6)

= (2^{2} + 6)(3^{2} + 6)(8^{2} + 6)(13^{2} + 6)(27^{2} + 6) = (6^{2} + 6)(12^{2} + 6)(463^{2} + 6)

= (8^{2} + 6)(12^{2} + 6)(13^{2} + 6)(27^{2} + 6) = (8^{2} + 6)(27^{2} + 6)(162^{2} + 6).

by Yoshio Mimura, Kobe, Japan

## 36804

36804^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36810

36810^{2} = (3^{2} + 9)(20^{2} + 9)(429^{2} + 9).

by Yoshio Mimura, Kobe, Japan

## 36864

36864 = 192^{2}, a square pegged by 6.

by Yoshio Mimura, Kobe, Japan

## 36882

36882^{2}± 5 are primes.

36882^{2} = (2^{2} + 5)(7^{2} + 5)(1673^{2} + 5).

by Yoshio Mimura, Kobe, Japan

## 36903

36903^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 36927

36927^{2}± 2 are primes.

by Yoshio Mimura, Kobe, Japan

## 36941

36941 ^{2} is the sum of (13x + 11)^{2} where x runs over 0, 1,..., 288.

by Yoshio Mimura, Kobe, Japan

## 36960

442^{2} + 36960 = 482^{2}, 442^{2} - 36960 = 398^{2}.

36960^{2} = (2^{2} - 1)(6^{2} - 1)(15^{2} - 1)(241^{2} - 1) = (3^{2} - 1)(6^{2} - 1)(34^{2} - 1)(65^{2} - 1)

= (3^{2} - 1)(9^{2} - 1)(34^{2} - 1)(43^{2} - 1) = (6^{2} - 1)(7^{2} - 1)(21^{2} - 1)(43^{2} - 1)

= (6^{2} - 1)(13^{2} - 1)(21^{2} - 1)(23^{2} - 1) = (9^{2} - 1)(21^{2} - 1)(197^{2} - 1) = (21^{2} - 1)(41^{2} - 1)(43^{2} - 1).

by Yoshio Mimura, Kobe, Japan

## 36964

36964^{2}± 3 are primes.

by Yoshio Mimura, Kobe, Japan

## 36966

36966^{2}± 5 are primes.

by Yoshio Mimura, Kobe, Japan

## 36975

36975^{2} = (22^{2} + 9)(36^{2} + 9)(46^{2} + 9).

by Yoshio Mimura, Kobe, Japan