SOLUTION: let (a,b,c) be a primitive pythagorous triplet(a<b<c).show that c is odd.

Question 475377: let (a,b,c) be a primitive pythagorous triplet(a
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
By the Pythagorean theorem,

Assume c is even. Then c^2 ≡ 0 (mod 4), and a^2 or b^2 can only be congruent to 0 or 1 mod 4, so this creates a contradiction (unless a,b,c are all divisible by 2, which still doesn't work since the triple is primitive). Hence, c must be odd.
RELATED QUESTIONS
let (a,b,c) be a primitive pythagorous triplet (a (answered by richard1234)
let m and n be two consicutive even integers and 1/m+1/n=p/q (in the lowest form) prove... (answered by richard1234)
Let A, B, and C be sets such that A union B = A union C and A intersect B = A intersect... (answered by moshiz08)
Let A, B, and C be sets. Show that (A − B) − C = (A − C) − (B... (answered by robertb)
Let A = {n C Z | n is odd} and B = {n C Z | n^2 - 1 mod 4}. Prove that A is included in... (answered by ikleyn)
Let a, b and c be sides of a triangle in arithmetic progression in this order. Show that... (answered by richard1234)
which triplet can not be the lengths of the 3 sides of a triangle and why? a)22,16,13... (answered by mananth)
Let a,b,c be real numbers satisfy ab + bc + ca = 1. Show that (a - b)/(1 + c^2) + (b -... (answered by Edwin McCravy)
Use the following set of 29 numbers to answer the questions.... (answered by solver91311)