\(A=5^{50}-5^{48}+5^{46}-5^{44}+...+5^6-5^4+5^2-1\)
\(A=\left(5^{50}-5^{48}\right)+\left(5^{46}-5^{44}\right)+...\left(5^6-5^4\right)+\left(5^2-1\right)\)
\(A=5^{50}\left(1+5^2\right)+5^{46}.\left(1+5^2\right)+...+5^6.\left(1+5^2\right)+5^2.\left(1+1\right)\)
\(A=5^{50}.26+5^{46}.26+...+5^6.26+5^2.2\)
\(A=26.\left(5^{50}+5^{46}+...+5^6+5^2\right)\)
Vì \(26.\left(5^{50}+5^{46}+...+5^6+5^2\right)\)chia cho 100 dư 26
Và 5 chia cho 100 dư 5
nên \(26.\left(5^{40}+5^{46}+...+5^6+5^2\right)\)chia cho 100 dư 21
