Question

是否存在整数a,b（a小于b）使其满足根号a+根号b=根号1476?带理由

Answer 1

由√a+√b=√1476=6√41,此时必有a=k^2*41且b=m^2*41,

即k√41+m√41=6√41,

于是得k+m=6,由a＜b且为正整数,则有

k=1,m=5,此时a=41,b=5^2*41=1025,

k=2,m=4,此时a=2^2*41=164,b=4^2*41=656.