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$(a_1^{b_1} \cdot a_2^{b_2} \cdots a_n^{b_n}) \;\; \text{mod} \;\; (c_1^{d_1} \cdot c_2^{d_2} \cdots c_m^{d_m})$

Would there be a way to find the modulo (preferably in the form of a prime number product; or the worst case value). I am not allowed to transform these products into integers, I have to work with the products... $a$ and $c$ are prime numbers and $b$ and $d$ are integers $> 0$. Products can be of different sizes (number of terms) Thank you

Giorgos Giapitzakis
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Bobi Piano
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    Re your preference: The result might be one very large prime, just below the modulus, even though $n$, $m$, the $a_i$, the $c_i$ are very small – Hagen von Eitzen Apr 08 '21 at 22:19
  • There are in theory but are they ever tedious ... – Roddy MacPhee Apr 08 '21 at 23:49
  • I noticed that ; let X be the left product and Y the right product ; X mod Y = PGCD x (numerator of the irreducible fraction X/Y % denominator of the irreducible fraction X/Y) . it simplifies a little the work if PGCD != 1, but it does not change too much the initial problem If you have an idea Roddy... – Bobi Piano Apr 09 '21 at 10:11

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