Recent questions and answers in Elementary Number Theory

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason RAssertion A: The order of the group ( $\mathrm{Z}_{5}, \times$ ) divid...

The remainder obtained when $\sum\limits_{m=1}^{2025} m!$ is divided by $18$ is$7$$9$$12$$16$

The number of factors of $2025$ (including $1$ and itself) equals$15$$25$$35$$45$ 

Let $b_{n} b_{n-1} \cdots b_{1}$ be the decimal representation of an $n$ digit number $m$. Let $b_{n} b_{n-1} \cdots b_{2}$ be the integer $a$ obtained from $m$ by stripp...

Consider the given number $(45)_{y}$ where $y$ is the base of the number. Some of the possible values of $y$ are given below.$5$$6$$7$$8$Choose the correct answer from th...

Let $m$ and $n$ are positive integers. ThenIf $n \neq 1$, then $m<mn$If $k$ is composite, then $k=m n$ where $1<m, n>k$If $mn=1$, then $m=1$ and $n=1$.If $k$ is composite...

What is the smallest positive integer that when multiplied with $2^{3} 3^{2} 4^{3} 5^{7} 6^{5}$ results in a perfect square?$6$$10$$15$$60$$210$ 

How many distinct factors does $2^{2} 3^{3} 4^{4} 5^{5}$ have? For example, $12$ has $6$ distinct fact ors: $1,2,3,4,6$, and $12$.$240$$264$$324$$360$None of the above 

For any positive integer $d$, the set\[\left\{10^{a}-10^{b} \mid a, b \text { are distinct positive integers }\right\}\]contains a multiple of $d$.

How many positive integers less than $1000$ are neither divisible by $3$ nor divisible by $5$? Explain how you arrived at your answer.

Let $b_{n} b_{n-1} \cdots b_{1}$ be the decimal representation of an $n$ digit number $m$. Let $b_{n} b_{n-1} \ldots b_{2}$ be the integer $a$ obtained from $m$ by stripp...