Maths Olympiad Prep

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Number theory Difficulty 5.3 AIME, harder Find the answer

9. Solve the following linear congruences using Euler's theorem
a) 5x≡3( mod 14)5 x \equiv 3(\bmod 14)
b) 4x≡7( mod 15)4 x \equiv 7(\bmod 15)
c) 3x≡5( mod 16)3 x \equiv 5(\bmod 16)

A number or a short expression. Spacing and $ signs are ignored.

Solution

9. a) x≡9( mod 14)x \equiv 9(\bmod 14)
b) x≡13( mod 15)x \equiv 13(\bmod 15)
c) x≡7( mod 16)x \equiv 7(\bmod 16)

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.