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Square of an Odd (Posted on 2002-10-06) Difficulty: 2 of 5
Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.

See The Solution Submitted by martyn    
Rating: 3.1333 (15 votes)

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Not factorial! | Comment 7 of 20 |
(In reply to Square of an Odd Number by Douglas Johnson)

Although your basic math is right, your definition of m! is wrong, so the equations N² = 8m! +1 and n = m! are wrong.

m! = m(m - 1)(m -2)...(3)(2)(1)

m(m+1)/2 = T(m), the mth triangle number (1,3,6,10...)

If you substitute T(m) everywhere that you used m!, then your answer would be correct.

Incidently T(m) is related to m!. T(m - 1) = C(m,2), where C(a,b) is the combination (usually indicated by stacking a over b like a fraction without the division bar, and enclosing them in parentases) and is equal to a!/b!(a - b)!
  Posted by TomM on 2002-10-07 19:16:26

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