List of top Mathematics Questions on Number Theory asked in CPET

Which one of the following options is the general solution(s) of the linear congruences \(x \equiv 1 \pmod{3}\), \(x \equiv 2 \pmod{5}\) and \(x \equiv 3 \pmod{7}\)?

If a, b are integers and p is a prime number, then which of the following statements is/are false?
(I) If \((a,p) = (b,p) = 1\) and \(a^k \equiv b^k \pmod{p}\) (\(k \in \mathbb{N}\)), then \(a \equiv b \pmod{p}\).
(II) If \((a,p) = 1\) and \(ax \equiv 1 \pmod{p}\), then \(a \equiv a^{p-2} \pmod{p}\).