The smallest squares containingk 70's :
2704 = 52²,   7070281 = 2659²,   5707047025 = 75545²,
4757070707041 = 2181071²,   7070867087048704 = 84088448².

The sum of the divisors of 70 is 12².

70² = (1)(2)(3 + 4)(5 + 6 + 7 + 8 + 9)(10).

70² = (1² + 6)(2² + 6)(8² + 6) = (2² + 6)(22² + 6).

70² = 1² + 2² + 3² + 4² + ... + 24².

70² = 1⁴ + 2⁴ + 3⁴ + 7⁴ + 7⁴.

70² = 4900, 4 = 2² and 900 = 30².

70² + 51² = 7501.

14^k + 1162^k + 1274^k + 2450^k are squares for k = 1,2,3 (70², 2996², 135436²).

Komachi equations:
70² = 9 - 8 + 7 * 654 + 321 = - 9 - 87 * 6 + 5432 - 1,
70² = - 1² + 2² - 3² + 4² * 5² + 67² - 8² + 9².

(1² + 2² + 3² + ... + 70²) = (1² + 2² + 3² + ... + 24²) + (1² + 2² + 3² + ... + 69²).

(70² - 2) = (8² - 2)(9² - 2).

(1 + 2 + ... + 38)(39 + 40 + ... + 57)(58 + 59 + ... + 70) = 23712².

70² = 4900 appears in the decimal expressions of π and e:
  π = 3.14159•••4900••• (from the 6216th digit),
  e = 2.71828•••4900••• (from the 7136th digit).

---

Page of Squares : First Upload February 16, 2004 ; Last Revised November 30, 2013
by Yoshio Mimura, Kobe, Japan