# Math Help - Find the remainder

1. ## Find the remainder

Find the remainder when $(144^{255}+192^{255})$ is divided by $49$

2. i tried using eulers theorem but cudnt proceed

3. Hello,

Note that 3*49=147, and thus 144=-3 mod 49.
And 4*49=196 ---> 192=-4 mod 49

So you're left to compute $-3^{255}-4^{255} (\bmod 49)$

But $\varphi(49)=6\times 7=42$

And $255=42\times 6+3$

So $3^{255}=(3^{42})^6\times 3^3\equiv 3^3 (\bmod 49)$

Similarly, $4^{255}\equiv 4^3 (\bmod 49)$

So $144^{255}+192^{255} \equiv -3^3-4^3 (\bmod 49) \equiv -27-64 (\bmod 49)\equiv -91\equiv 7 (\bmod 49)$

The remainder is 4

4. thanks

jus a small typo from ur side

$4^3=64$

u wrote $67$

so remainder shud be $7$