OFFSET
1,1
COMMENTS
The corresponding even legs are given in 4*A253805.
The legs of the other Pythagorean triangle with hypotenuse A080109(n) are given A253802(n) (odd) and A253803(n) (even).
Each fourth power of a prime of the form 1 (mod 4) (see A002144(n)^= A080175(n)) has exactly two representations as sum of two positive squares (Fermat). See the Dickson reference, (B) on p. 227.
This means that there are exactly two Pythagorean triangles (modulo leg exchange) for each hypotenuse A080109(n) = A002144(n)^2, n >= 1. See the Dickson reference, (A) on p. 227.
Concerning the primitivity question of these triangles see a comment on A253802.
REFERENCES
L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.
FORMULA
EXAMPLE
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 16 2015
STATUS
approved