The smallest squares containingk 79's :
7921 = 89²,   10797796 = 3286²,   15679797961 = 125219²,
7979867917956 = 2824866²,   2379797967947929 = 48783173².

The 4th integer which is the sum of 5 distinct squares.

79² = 6241, a zigzag square with different digits.

1² + 2² + 3² + ... + 79² = 167480, which consists of different digits.

79² = 1! + 5! + 5! + 5! + 5! + 6! + 7!.

79² = 6241, 6³ + 2³ + 4³ + 1³ = 17²,
79² = 6241, 6 + 2 + 41 = 7²,
79² = 6241, 624 + 1 = 25².

79⁸ = 1517108809906561, 1 + 5171 + 08 + 8 + 0990 + 6 + 56 + 1 = 79²,
79⁸ = 1517108809906561, 1 + 5171 + 08 + 80 + 9 + 906 + 5 + 61 = 79²,
79⁸ = 1517108809906561, 1 + 5171 + 088 + 09 + 906 + 5 + 61 = 79².

A 3-by-3 magic square consisting of different squares with constant 79²:

Komachi Fraction : (79/2)² = 954873/612.

Komachi equations:
79² = 1234 * 5 + 6 + 7 * 8 + 9 = 1234 * 5 + 6 - 7 + 8 * 9
  = 1 + 2 * 3 * 4 * 5 * 6 * 78 / 9 = 12 * 3 * 4 - 5 + 678 * 9
  = 987 * 6 - 5 + 4 + 32 * 10,
79² = 12² + 3² - 4² - 5² - 6² + 78² + 9² = 9² + 8² + 76² + 54² / 3² - 2² */ 1²
  = 98² - 7² * 6² - 5² / 4² * 32² + 1² = - 9² + 8² * 7² + 65² - 4² - 32² + 1²
  = - 9² - 8² + 76² + 5² + 4² * 3² + 21² = 9² * 8² - 7² * 6² + 54² + 3² - 2² - 10²,
79² = 1⁴ + 2⁴ - 3⁴ - 4⁴ + 56⁴ - 7⁴ * 8⁴ + 9⁴ = 1⁴ + 2⁴ - 3⁴ - 4⁴ + 56⁴ / 7⁴ - 8⁴ + 9⁴
  = 1⁴ + 2⁴ - 3⁴ - 4⁴ + 56⁴ / 7⁴ / 8⁴ * 9⁴ = 1⁴ + 2⁴ - 3⁴ - 4⁴ - 56⁴ + 7⁴ * 8⁴ + 9⁴
  = 1⁴ + 2⁴ - 3⁴ - 4⁴ - 56⁴ / 7⁴ + 8⁴ + 9⁴ = 1⁴ + 2⁴ - 3⁴ - 4⁴ * 56⁴ / 7⁴ / 8⁴ + 9⁴
  = 1⁴ + 2⁴ - 3⁴ - 4⁴ / 56⁴ * 7⁴ * 8⁴ + 9⁴ = 1⁴ * 2⁴ - 3⁴ - 4⁴ + 56⁴ / 7⁴ / 8⁴ + 9⁴.

1² + 2² + 3² + 4² + ... + 79² = 167480, which consists of different digits.

(79² + 7) = (8² + 7)(9² + 7) = (1² + 7)(2² + 7)(8² + 7).

(1 + 2 + ... + 7)(8 + 9 + ... + 16)(17 + 18 + ... + 79) = 3024²,
(1 + 2 + ... + 24)(25 + 26 + ... + 30)(31 + 32 + ... + 79) = 11550²,
(1 + 2 + ... + 44)(45 + 46 + ... + 55)(56 + 57 + ... + 79) = 29700².

79² = 6241 appears in the decimal expressions of π and e:
  π = 3.14159•••6241••• (from the 1706th digit),
  (6241 is the ninth 4-digit square in the expression of π,)
  e = 2.71828•••6241••• (from the 7248th digit).

(1²)(2² + 3² + ... + 71²)(72²)(73² + 74² + ... + 79²) = 5055120².

---

Page of Squares : First Upload February 23, 2004 ; Last Revised April 1, 2010
by Yoshio Mimura, Kobe, Japan