Dân chuyên toán vô đây ^ _ ^

T

thienlong_cuong

222^333 + 333^222

= 111^333 . 2^333 + 111^222 . 3^222

= 111^222.( 111^111.2^333 + 3^222)

= 111^222 .{ [111.(2^3)]^111 + (3^2)^111}

= 111^222 . ( 888^111 + 9^111 )

Ta xet
888^111 + 9^111

=( 888 + 9).[8^110 - (8^109).9 + (8^108).(9^2) -....- 888.(9^109) + 9^110)

= 897 . [ 8^110 -(8^109).9 + (8^108)(9^2) -....- 888.(9^109) + 9^110

= 13.69.[ 8^110 -(8^109).9 + (8^108)(9^2)-...- 888.(9^109) + 9^110
chia he^t 13

=> 888^111 + 999^111 chia het 13
=> 111^222 . ( 888^111 + 9^111 ) chia he^t 13
Hay
222^333 + 333^222 chia he^t 13 (ok)

Nho thanks
 
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