perplexus.info :: Just Math : 2 ways to prove it

2 ways to prove it (Posted on 2017-10-31)

For every positive integer n: 10ⁿ+18*n-1 is divisible by 27.

The above statement can be proven by more than one way.

Find at least 2 distinct methods.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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Method 1

| Comment 1 of 4

(10ⁿ+18*n-1)/9 (mod 3) = ((10ⁿ-1)/9 (mod 3) + (18*n)/9 (mod 3) = n (mod 3) + 2*n (mod 3) = 3*n (mod 3) = 0

Posted by chun on 2017-10-31 12:29:13

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