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Factor the integer n = 13231 (= 101 * 131) by taking advantage of the relations (all modulo n): 1...

Factor the integer n = 13231 (= 101 * 131) by taking advantage of the relations (all modulo n): 122^2 = 3 * 19 * 29, 124^2 = 3 * 5 * 11 * 13, 125^2 = 2 * 3^2 * 7 * 19, 126^2 = 5 * 23^2, 127^2 = 2 * 3^2 * 7 * 23, 129^2 = 2 * 5 * 11 * 31, 134^2 = 3^3 * 5^2 * 7, 136^2 = 3^4 * 5 * 13, 139^2 = 2 * 3 * 5 * 7 * 29, 141^2 = 2 * 5^2 * 7 * 19, 146^2 = 3 * 5 * 7^2 * 11, 149^2 = 2 * 3 * 5 * 13 * 23 and linear algebra on exponents of the prime factorizations.

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as al= (o 13231 ) аз-Up (mod a 7675 med 1323 4272 8 mod 132 31) a2ahy Ato we check ニ gcd (9,13231) (99 , 13231) 9-cd :gcA(7171, 3231) str a aed (23 22, 132 3)) 0101 > So 16 1

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