What is the smallest positive integer which leaves remainders of 3, 4 and 5 when divided respectively by 5, 7 and 9?

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Let the number be x. x/5 = p +3 as remainder x/7 = q +4 as remainder x/9 = r +5 as remainder or x = 5p + 3 … (1) x = 7q + 4 .. (2) x = 9r + 5 … (3) We can assign different integers to say any term: r in (3), and see (2) and (3) give p and q as integers. After a few trials i found...
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Let the number be x. x/5 = p +3 as remainder x/7 = q +4 as remainder x/9 = r +5 as remainder or x = 5p + 3 … (1) x = 7q + 4 .. (2) x = 9r + 5 … (3) We can assign different integers to say any term: r in (3), and see (2) and (3) give p and q as integers. After a few trials i found r= 17 and corresponding values of p to be 31 and q to be 22. Thus x = 158. read less
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