Modulus

The remainder of the quotient of two numbers (usually integers).

Primes

Primes or prime numbers are integers greater than 1 which are divisible only by themselves and 1, i.e.: 2, 3, 5, 7, 11, ..



Several ways notation

Example

"If a higher power of 3 also divided more than one modulus we would need to check those higher powers as well. for each primes that we discovered and each modulus we find the highest power of that primes that divides the modulus"

from question  

System of congruences with non-pairwise coprime moduli

"There are several ways to do that. we find that 3 is the only primes that divides more than one modulus and the highest power of that primes that divides more than one modulus is i use the notation for exponentiation used in python and fortran for clarity since the caret also has other uses in computers. that could prevent your system of equations from having any solution at all"

from question  

System of congruences with non-pairwise coprime moduli

Others

Example

We also add the new equations we get for each power of the primes that divides more than one modulus

from question  

System of congruences with non-pairwise coprime moduli

It is perfectly possible to use rsa with a modulus n that is composed of more than two primes factors p and q but two things have to be noted

from question  

Integer factorization and cryptography

The linear congruential generator explores every value less than the modulus when the multiplier and modulus are relatively primes

from question  

Writing a strided x86 benchmark

In particular original ntt required to find primes n as the working modulus that is larger than so that the result never overflows

from question  

Implementing FFT over finite fields

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