JEE MAIN - Mathematics (2023 - 8th April Evening Shift - No. 2)
$$25^{190}-19^{190}-8^{190}+2^{190}$$ is divisible by :
14 but not by 34
neither 14 nor 34
both 14 and 34
34 but not by 14
Explanation
The given expression is divisible by 6 and 17 .
Also, $25^{190}-8^{190}$ is not divisible by 7
but $19^{190}-2^{190}$ is divisible by 7 ,
So, $25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by 34 but not by 14 .
Also, $25^{190}-8^{190}$ is not divisible by 7
but $19^{190}-2^{190}$ is divisible by 7 ,
So, $25^{190}-19^{190}-8^{190}+2^{190}$ is divisible by 34 but not by 14 .
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