Find smallest natural numbers $x,y$ such that
$$ 49x = 125y.$$
Will this require some special modular arithmetic property or am I missing something?
Asked
Active
Viewed 41 times
0
-
x=125n and y=49n for any integer n. – Alessio K Jan 24 '20 at 20:17
-
@DietrichBurde 0 is not being considered a natural number here – Jan 24 '20 at 20:18
-
If you must use modular arithmetic than $, n\equiv 0\pmod{!49\ &\ 125}\iff n\equiv 0\pmod{!45\cdot 125}\ $ by CCRT – Bill Dubuque Jan 24 '20 at 21:21
1 Answers
0
Not at all: it only requires high school arithmetic. This common number is nothing else than the l.c.m. of $49$ and $125$. Now these numbers are coprime, so …
metamorphy
- 39,111
Bernard
- 175,478