已知 {an}\left\{ {a}_{n}\right\}{an} 为等差数列, {bn}\left\{ {b}_{n}\right\}{bn} 是公比为 2 的等比数列,且 a2−b2=a3−b3=b4−a4{a}_{2} - {b}_{2} = {a}_{3} - {b}_{3} = {b}_{4} - {a}_{4}a2−b2=a3−b3=b4−a4 .(1) 证明： a1=b1{a}_{1} = {b}_{1}a1=b1 ；(2) 求集合 {k∣bk=am+a1,1≤m≤500}\left\{ {k \mid {b}_{k} = {a}_{m} + {a}_{1},1 \leq m \leq {500}}\right\}{k∣bk=am+a1,1≤m≤500} 中元素个数.