Integers congruent to last two decimal digits mod 23

enzocreti · 2020-03-03, 10:13

N belongs to Z, that is N can be every positive, negative or 0 integer.
let be m the last two digits of N

so for exampe if N=9345, m=45
is it possible to find with a program the numbers N congruent to m mod 23?
Is it possible to extend this to other primes p different from 23?

Dylan14 · 2020-03-03, 18:38

Quote:

Originally Posted by enzocreti

is it possible to find with a program the numbers N congruent to m mod 23?

Yes. I wrote this Python script to determine said numbers:

Code:

#program to check if a number is congruent to its last 2 decimal digits mod p,
#where p is a prime

N = -10000
p = 23
while(N<=10000):
    stringint = str(N)
    finaldigits = stringint[-2:]
    finaldigitsint = int(finaldigits)
    if N%p == finaldigitsint:
        print(N)
        N += 1
    else:
        N += 1

Up to |N| = 10000 I get the following numbers:

Code:

If you have a Python interpreter you can run this with a different value of p to find numbers that are congruent to their last 2 digits mod p.
That being said, it may be worth learning a coding language so you don't have to ask such questions. It's one thing for someone else to do the code, it's another to do it yourself.

2020-03-03, 10:13	#1
enzocreti Mar 2018 1033₈ Posts	Integers congruent to last two decimal digits mod 23 N belongs to Z, that is N can be every positive, negative or 0 integer. let be m the last two digits of N so for exampe if N=9345, m=45 is it possible to find with a program the numbers N congruent to m mod 23? Is it possible to extend this to other primes p different from 23? Last fiddled with by enzocreti on 2020-03-03 at 10:14

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