Math Problem Statement

500^2 mod 256961 = 250000 = 2^4 * 5^6 501^2 mod 256961 = 251001 = 3 * 167 * 501 502^2 mod 256961 = 252004 = 2^2 * 13 * 967 503^2 mod 256961 = 253009 = 253009 504^2 mod 256961 = 254016 = 2^6 * 3^4 * 7^2 505^2 mod 256961 = 255025 = 5^2 * 7^2 * 11 506^2 mod 256961 = 256036 = 2^2 * 11^2 * 23^2 507^2 mod 256961 = 88 = 2^3 * 11^1 508^2 mod 256961 = 1103 = 19 * 29 * 2 509^2 mod 256961 = 2120 = 2^3 * 5 * 53 510^2 mod 256961 = 3139 = 19 * 23 * 7 511^2 mod 256961 = 4160 = 2^5 * 5 * 13 512^2 mod 256961 = 5183 = 23 * 11 * 13 513^2 mod 256961 = 6208 = 2^7 * 97 514^2 mod 256961 = 7235 = 5^1 * 7 * 13 * 17 515^2 mod 256961 = 8264 = 2^3 * 1033 516^2 mod 256961 = 9295 = 5^1 * 19 * 97 517^2 mod 256961 = 10328 = 2^3 * 7 * 23 * 13 518^2 mod 256961 = 11363 = 11^1 * 1033 519^2 mod 256961 = 12400 = 2^3 * 1549 520^2 mod 256961 = 13439 = 29 * 463 521^2 mod 256961 = 14480 = 2^4 * 5^1 * 19 * 7 522^2 mod 256961 = 15523 = 19^2 * -1^1 523^2 mod 256961 = 16568 = 2^3 * 7 * 59 524^2 mod 256961 = 17615 = 5^1 * 13^1 * -1^1 525^2 mod 256961 = 18664 = 2^3 * -1^1

Solution

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Math Problem Analysis

Mathematical Concepts

Modular Arithmetic
Prime Factorization
Quadratic Residues

Formulas

n^2 mod m

Theorems

Chinese Remainder Theorem
Prime Factorization Theorem
Quadratic Residue Theorem

Suitable Grade Level

University Level