perplexus.info :: Just Math : Extended Divisibility

Extended Divisibility (Posted on 2025-01-31)

Let n and m be integer numbers. Prove that, if 3n+7m is divisible by 19, then the number 43n + 75m is divisible by 19 also.

No Solution Yet Submitted by Danish Ahmed Khan

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Analytic Solution

Comment 2 of 2 |

Though the solution space is small enough to use a spreadsheet like Larry did, we don't even need that much. Start with the given condition and do some modular arithmetic.

3n + 7m = 0 mod 19

8*(3n + 7m) = 8*0 mod 19

24n + 56m = 0 mod 19

(19n + 19m) + 24n + 56m = (19n + 19m) + 0 mod 19

43n + 75m = 0 mod 19

Posted by Brian Smith on 2025-01-31 11:14:02

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