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Deffense [45]
2 years ago
7

Prove: The square of a number that is

Mathematics
1 answer:
Nikolay [14]2 years ago
3 0

Let 3<em>n</em> + 1 denote the "number" in question. The claim is that

(3<em>n</em> + 1)² = 3<em>m</em> + 1

for some integer <em>m</em>.

Now,

(3<em>n</em> + 1)² = (3<em>n</em>)² + 2 (3<em>n</em>) + 1²

… = 9<em>n</em>² + 6<em>n</em> + 1

… = 3<em>n</em> (3<em>n</em> + 2) + 1

… = 3<em>m</em> + 1

where we take <em>m</em> = <em>n</em> (3<em>n</em> + 2).

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