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Colt1911 [192]
3 years ago
11

Prove that (n+5)^2 - (n+3)^2 is a multiple of 4 for all positive integer values of n.

Mathematics
1 answer:
Drupady [299]3 years ago
3 0

Answer:

(n+5)² - (n+3)² =

= (n² + 10n + 25) - (n² + 6n + 9)

= n² + 10n + 25 - n² - 6n - 9

= 4n + 16

= 4(n + 4) ⋮ 4

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