Pythagorean TriplesDate: 04/14/97 at 09:05:48 From: Paul W. Paulsen Subject: Pythagorean Triples At a recent Parent-Teacher Conference Night a parent asked me why, in a Pythagorean triple (e.g. 3,4,5), the three numbers cannot all be prime. Is this possible? Example? Why not? Thanks. Paul Paulsen Date: 04/14/97 at 10:25:08 From: Doctor Mitteldorf Subject: Re: Pythagorean Triples Dear Paul, If you think "prime" it makes it sound like a high-falutin' result from number theory. Think "even" and "odd" instead. If a^2 + b^2 = c^2, then a, b, and c cannot all be odd. If a and b are odd, then c is even, as it is the square root of the sum of two odd numbers. This leaves only cases where a = 2 or b = 2, since 2 is the only even prime. Notice that squares get increasingly far apart, so 1 and 4 differ by 3, but every other pair of squares differs by at least 5. -Doctor Mitteldorf, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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