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Perhaps (yes, perhaps... I may be At Fault here) your intended question is slightly different from the way you wrote it. Since I don't know exactly what that question is, I will answer the question that you wrote.

43n + (83)(923n)-1=43n+76609n-1=76652n-1.

Say that n=1. Then you have 76652(1)-1=76652-1=76651.

76651 is not divisible by 7, so I have contradicted your postulate.

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Q: Show that 43n plus 83x923n-1 is divisible by 7 for all positive integers n I know that you have to use modulo 7 in this question if you use it please explain why. please use very simple terms?
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