25¹⁹⁰ -19¹⁹⁰ - 8¹⁹⁰ + 2¹⁹⁰ is divisible by

25¹⁹⁰ + 2¹⁹⁰ - 19¹⁹⁰ - 8¹⁹⁰
$=\underbrace{\left({25}^{190}-{19}^{190}\right)}-\underbrace{\left(8^{190}-2^{190}\right)}$
divisible by 6
$\underbrace{\left({25}^{190}-8^{190}\right)-\left({19}^{190}-2^{190}\right)}$
divisible by 17
$\Rightarrow$divisible by 34
And (25¹⁹⁰ - 8¹⁹⁰) is not divisible by 7
But (19¹⁹⁰ - 2¹⁹⁰) is divisible by 7
so 25¹⁹⁰ + 2¹⁹⁰ - 19¹⁹⁰ - 0¹⁹⁰
Is divisible by 34 but not by 14