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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