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Extended Divisibility (Posted on 2025-01-31) Difficulty: 2 of 5
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    
Rating: 5.0000 (1 votes)

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Solution Answer Comment 3 of 3 |
Suppose 19|3n+7m. Then, 19|8(3n+7m)=24n+56m. Since 19|19n+19m, then 19|(24n+56m)+(19n+19m)=43n+75m. Therefore, if 19|3n+7m, then 19|43n+75m.


  Posted by Math Man on 2025-02-07 17:33:36
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