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MMO 323 Moscow MO 1956 integer that divides (5m + 6), (8m + 7)

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August 19, 2019
number theoryDividedivisor

Problem Statement

a) Find all integers that can divide both the numerator and denominator of the ratio 5m+68m+7\frac{5m + 6}{8m + 7} for an integer mm.
b) Let a,b,c,d,ma, b, c, d, m be integers. Prove that if the numerator and denominator of the ratio am+bcm+d\frac{am + b}{cm+ d} are both divisible by kk, then so is ad−bcad - bc.
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