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What is the largest positive integer n such that 1457 and 1754 leave the same remainder when divided by n?

 Apr 16, 2019
 #1
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+1

n=1; a=(1457 % n);b=(1754%n);if(a==b, goto4,goto5);printa,b,n; n++; if(n<2000, goto1, discard=0;
Rem       n
0 0           1
2 2           3
8 8           9
5 5          11
26 26      27
5 5           33
71 71      99
269 269  297

So, the largest n = 297 with a remainder of 269

 Apr 16, 2019
 #2
avatar+23273 
+2

What is the largest positive integer n such that 1457 and 1754 leave the same remainder when divided by n?

 

see: https://web2.0calc.com/questions/a-nbsp-what-is-the-largest-positive-integer-n-such-that-1457-and-1754-leave-the-same-remainder-when-divided-by-n

 

laugh

 Apr 18, 2019
 #3
avatar+105463 
+1

Thanks Heureka and guest.

I was wondering how to do this.  Modular arithmetic is one of the areas that I want to learn more about :)

It is a pity there is not a million hours in a day, I'd use 80% of them for learning things, and I'd still have time to goof off.  LOL.

Melody  Apr 18, 2019
 #4
avatar+23273 
+2

Thank you, Melody !

 

laugh

heureka  Apr 18, 2019

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