+2651 Let $a$ be an integer such that $a \equiv 5 \pmod{7}$. Find the value of $a + 1 \pmod{7}$. Express your answer as a residue between $0$ and the modulus.
+1804 mmm...not sure about my solution, but here it is.
First, we have the modulo
\(a \equiv 5 \pmod{7}\)
Since we must find a+1 mod 7, let's add 1 to both sides of our equation to get
\(a+1 \equiv 5+1 \pmod7\\ a+1 \equiv 6 \pmod7\)
We can test numbers.
Let's test 5, 19, 26
\(6 \equiv 6\pmod7\\ 20 \equiv 6 \pmod 7\\ 27 \equiv 6 \pmod 7\)
So 6 is our answer.
Thanks! :)
