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AMC / AIME · Modular Arithmetic · AIME / USAJMO / AMO

Modular Arithmetic: (Proof track.) Prove the Chinese Remainder Theorem for pairwise coprime moduli, then find the unique math with math, mat

Congruences and power cycles.

Try the problem

**(Proof track.)** Prove the Chinese Remainder Theorem for pairwise coprime moduli, then find the unique n∈(0,5⋅7⋅8]n\in(0,5\cdot7\cdot8] with n≡1(mod5)n\equiv1\pmod5, n≡2(mod7)n\equiv2\pmod7, n≡3(mod8)n\equiv3\pmod8. Enter nn.

Hint and answer

Concept to use

Orders and Fermat.

Hint

Solve stepwise CRT.

Answer

157

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