MathCastle
Number TheoryHardThe Chinese Remainder Theorem

The Chinese Remainder Theorem · Hard problem

For which values of aa with 0≤a<150 \le a < 15 does the system x≡a(mod15)x \equiv a \pmod{15}, x≡7(mod21)x \equiv 7 \pmod{21} have a solution? Give the sum of all such aa.