... =2u2 and c − a =2v2,wefind b2=4u2v2 and b =2uv, c = u2+ v2,anda = u2− v2, where, since a and care odd and coprime, u and v must be of opposite parity and coprime. Also, u and vmay ... for a, b,andc are satisfied if and only if l, m,andn are positive. In termsof l, m,andn, eqn (1.5.1) reduces tolmn = 16(l + m + n) . (1.5.2)Note that for a, b,andc to be integers l, m,andn have ... parity, and from eqn (1.5.2) it is evident that they must all be even. So, puttingl =2p, m =2q,andn =2r,wehavea = q + r, b = r + p,andc = p + q,wherep,q,andr satisfy pqr =4(p + q + r) and p, q,andr...