The remainder when 7^2+7^22+7^23+7^24 is divided by 25 is 0. To prove this, we first factor out the factor that is common to the terms of this mathematical expression. The common term is 7^21. The expression them become 7^21(1+7+7^2+7^3). We now have an expression that is easier to calculate. (1+7+7^2+7^3) is equal to 400, since 400 is divisible by 25, we can say that the value of the expression is divisible by 25.