# Product of Totatives-III Divisors of Googol

Number Theory Level pending

For a positive integer $$n$$, let $$\mathbb P(n)$$ be the product of all possible positive integers $$a \leq n$$ with $$\gcd(a,n)=1$$.

Find the number of all possible distinct positive divisors $$d$$ of $$10^{100}$$ such that $\mathbb P(d) \equiv 1 \pmod{d}$

Suggested Warm-Ups: This and this.

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