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1969 IMO Problems/Problem 1

Revision as of 18:26, 7 February 2011 by Thrax (talk | contribs) (Created page with 'The equation was<math>z = n^4 + a</math> ,you can put <math> a = 4 m^4 </math> for all natural numbers m. So you will get <math> z = n^4 + 4 m^4 = n^4+4m^4 +4n^2 m^2 - 4n^2 m^2</…')
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The equation was$z = n^4 + a$ ,you can put $a = 4 m^4$ for all natural numbers m. So you will get $z = n^4 + 4 m^4 = n^4+4m^4 +4n^2 m^2 - 4n^2 m^2$ $z = (n^2+2 m^2)^2 - (2nm)^2 = (n^2+2 m^2 -2nm)(n^2+2 m^2 +2nm)$ so you get z is composite for all $a = 4 m^4$

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