Show that the number 9^{8n+4}-7^{8n+4} is divisible by 20 for any natural numbers n

Collected in the board: Number Theory

Steven Zheng posted 4 months ago






which shows the number could be factored to at least 2 factors.

The first factor is difference of two odd numbers which will result in a even number.

The second factor is the sum of 81^{2n+1}+49^{2n+1}

The ones place of 81^{2n+1} is 1. The ones place of 49^{2n+1} is 9. Their sum is 10


9^{8n+4}-7^{8n+4} is divisible by both 2 and 10 simultaneously, hence, divisible by 20

Steven Zheng posted 4 months ago

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