Browse · MATH Print → jmc number theory senior Problem Suppose a is an integer such that 0≤a≤14, and 23593562374−a is a multiple of 15. What is a? Solution — click to reveal Note that 23593562374=3+2(74)+6(74)2+5(74)3+3(74)4+9(74)5+5(74)6 +3(74)7+2(74)8. But 74≡−1mod15, so this is just 3−2+6−5+3−9+5−3+2=0mod15, so a=0. Final answer 0 ← Previous problem Next problem →