Maths Olympiad Prep

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Number theory Difficulty 5.5 AIME, harder Find the answer

17. Find the number of incongruent solutions of
a) x231(mod75)x^{2} \equiv 31 \quad(\bmod 75)
b) x216(mod105)x^{2} \equiv 16 \quad(\bmod 105)
c) x246(mod231)x^{2} \equiv 46 \quad(\bmod 231)
d) x21156(mod325375116)\quad x^{2} \equiv 1156\left(\bmod 3^{2} 5^{3} 7^{5} 11^{6}\right).

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

None

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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.