Home › UP Board Class 10 › mathematics › numbertheory › The square of any odd integer, when divided by 8…
The square of any odd integer, when divided by 8, leaves remainder
A3
B5
C0
D1
Answer & Solution
Correct answer: D. 1
An odd integer is $2k+1$; its square is $4k(k+1)+1$. Since $k(k+1)$ is even, $4k(k+1)$ is a multiple of 8, so the square is $\equiv 1 \pmod 8$.
Related questions
If $3^x = 4^y = 12^z$ with $x,y,z$ nonzero, then $\dfrac{1}{z}$ equalsThe HCF of two consecutive positive integers isTwo positive integers have HCF 9 and LCM 90. If one number is 18, the other isThe remainder when $2^{100}$ is divided by 7 isWhich of the following is an irrational number?If $a = 2^3 \cdot 3^4 \cdot 5^2$ and $b = 2^4 \cdot 3^2 \cdot 7$, then $\dfrac{\text{LCM}(If $n$ is a natural number, then $6^n$ can never end with the digitThe smallest positive integer that is divisible by every integer from 1 to 10 is