摘要:设m是正偶数.证明了(A)若b是奇素数,且a=m"m6-21m4+35m2-7|, b=|7m6-35m4+ 21m2-1|,c=m2+1,则Diophantine方程G: ax +by=cz仅有正整数解(x,y,z)=(2,2,7):(B)若m> 2863,且a=m|m8-36m6+126m4-84m2+9|, b=|9m8-84m6+126m4-36m2+l|,c=m2+1,则Diophantine方程G仅有正整数解(x,y,z)=(2,2,9);(C)若a,b,c适合a=m|Σr-1/2i=0(-1)i(r2i)mr-2i-1|,b=|Σr-1/2i=0(-1)i(r2i+1)mr-2i-1|,c=m2+1, r≡1 (mod4), 2|x, 2|y,且b为奇素数或m>145r(logr),则方程G仅有解(x,y,z)=(2,2,r).