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Solve: x is congruent with 5 (mod6), x is congruent with 5 (mod13), x is congruent with...

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Solve: x is congruent with 5 (mod6), x is congruent with 5 (mod13), x is congruent with 4 (mod 5)

 

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x=6m+5

x=13n+5

So x=78o+5

78o+5 mod 5 = 3o

3o = 5p+4

The smallest number that makes this true is o=3, p = 1

So the answer is

x = 78(3)+5=234+5=239

239 mod 6 = 5

239 mod 13 = 5

239 mod 5 = 4

So the answer is (5*6*13)p+239=390p+239 where p is an integer

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