If you look at the table of primitive Pythagorean triples, you will see many tri

Question

If you look at the table of primitive Pythagorean triples, you will see many triples in which c is 2 greater than a. For example, the triples (3, 4, 5), (15, 8, 17), (35, 12, 37), and (63, 16, 65) all have this property.

a) find two more primitive Pythagorean triples (a, b, c) haveing c=a +2.
b) find a primitive Pythagorean triple (a, b, c) having c= a+2 and c > 1000.
c) try to find a formula that describes all primitive Pythagorean triples (a, b, c) having c= a+2

Explanation / Answer

a) first triplet is (48,14,50) second triplet is (80,18,82) b) for c>1000 the triplet is (1023,64,1025) c) a=(n^2)-1 b=2n c=(n^2)+1 where n>1 a,b,c is a pythagoreans triplet

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