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AMC / AIME · Modular Arithmetic · Medium

Modular Arithmetic: Find the smallest positive integer math with math and math.

Congruences and power cycles.

Try the problem

Find the smallest positive integer nn with n≡2(mod5)n\equiv 2\pmod 5 and n≡3(mod7)n\equiv 3\pmod 7.

Hint and answer

Concept to use

Units digits / cycles.

Hint

Check 2,7,12,17,…2,7,12,17,\ldots mod 77.

Answer

17

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