MathCastle
Number TheorySuperchallengeThe Chinese Remainder Theorem

The Chinese Remainder Theorem · Superchallenge problem

How many triples (a,b,c)(a, b, c) with 0≤a<40 \le a < 4, 0≤b<60 \le b < 6, 0≤c<90 \le c < 9 make the system x≡a(mod4)x \equiv a \pmod 4, x≡b(mod6)x \equiv b \pmod 6, x≡c(mod9)x \equiv c \pmod 9 solvable?