Let n be a non-negative integer. Then the number of divisors of the form 4 n + 1 of the number 10 10 ·…

Let $N=2^{10}\times 5^{10}\times {11}^{11}\times {13}^{13}$

Now, power of $2$ must be zero,

Power of $5$ can be anything,

Power of $13$ can be anything.

But, power of $11$ should be even.

So, required number of divisors is

$1\times 11\times 14\times 6=924.$