Question

How many positive integers N from 1 to 5000 satisfy the congruence N \equiv 5 \pmod{12}?

Answer 1

actually, it is N==5(mod 12) the "=="sign means congruent.

Answer 2

\(\large \begin{aligned} \color{black}{

N\equiv 5\pmod {12}\\~\\
N=12k+5\\~\\
\normalsize \text{for integers between 1 and 5000}\\
\implies 1\leq 12k+5\leq 5000

}\end{aligned}\)

Answer 3

I think it will simplify to -4<12k<4995. which also simplifies to 1<k<416. total 417... right! I got it!

Answer 4

was it 417

Answer 5

i m getting \(416\)

Answer 6

or may be i m wrong