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AMC / AIME · Modular Arithmetic · Hard

Modular Arithmetic: Number of solutions to math.

Congruences and power cycles.

Try the problem

Number of solutions to x2≡1(mod100)x^2\equiv1\pmod{100}.

Hint and answer

Concept to use

CRT systems.

Hint

CRT mod 4,254,25.

Answer

4

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