Newbetuts

Prove for every three integers $a$, $b$ and $c$ that an even number of the integers $a + b$, $a + c $and $b + c$ are odd. [duplicate]

How and what to teach on a first year elementary number theory course?

How many zeroes are there at the end of the sum $1^1 + 2^2 + 3^3 + \cdots+ 100^{100}$?

Computing the last non-zero digit of ${1027 \choose 41}$?

An upper bound for Summative Fission numbers

Prove that $(\sqrt2 − 1)^n, \forall n \in \mathbb{Z^+}$ can be represented as $\sqrt{m} − \sqrt{m−1}$ for some $m \in \mathbb{Z^+}$ (no induction).

How many natural number between $100$ and $1000$ exist which can be expressed as sum of 10 different primes.

Prove $2^{1/3} + 2^{2/3}$ is irrational

Is the finite sum of factorials constant modulo the summation limit?

Proving that this function has the same value for all integers $\geq4$. [duplicate]

How many Unique numbers?

How do I find $a,b\in\mathbb{Z}$ s.t. $\{ac-bd+i(ad+bc)\mid c, d\in\mathbb{Z}\}$ have real and imaginary parts both even or both odd?

squeeze the floor value of a finite series [duplicate]

Determine all integers $x,\ y,\ z$ that satisfy $x+y+z=(x-y)^{2}+(y-z)^{2}+(z-x)^{2}$

If $y^2-x^2\bigm|2^ky-1$ and $2^k-1\bigm|y-1$ then $y=2^k$ and $x=1$

Finding all natural $x$, $y$, $z$ satisfying $7^x+1=3^y+5^z$

New posts in elementary-number-theory

When is Euler's totient function for two different integers equal?

Prove by induction that $5^n - 1$ is divisible by $4$.

Continued Fraction [1,1,1,...]

Is there a conjecture with maximal prime gaps

Prove for every three integers $a$, $b$ and $c$ that an even number of the integers $a + b$, $a + c $and $b + c$ are odd. [duplicate]

How and what to teach on a first year elementary number theory course?

How many zeroes are there at the end of the sum $1^1 + 2^2 + 3^3 + \cdots+ 100^{100}$?

Computing the last non-zero digit of ${1027 \choose 41}$?

An upper bound for Summative Fission numbers

Prove that $(\sqrt2 − 1)^n, \forall n \in \mathbb{Z^+}$ can be represented as $\sqrt{m} − \sqrt{m−1}$ for some $m \in \mathbb{Z^+}$ (no induction).

How many natural number between $100$ and $1000$ exist which can be expressed as sum of 10 different primes.

Prove $2^{1/3} + 2^{2/3}$ is irrational

Is the finite sum of factorials constant modulo the summation limit?

Proving that this function has the same value for all integers $\geq4$. [duplicate]

How many Unique numbers?

How do I find $a,b\in\mathbb{Z}$ s.t. $\{ac-bd+i(ad+bc)\mid c, d\in\mathbb{Z}\}$ have real and imaginary parts both even or both odd?

squeeze the floor value of a finite series [duplicate]

Determine all integers $x,\ y,\ z$ that satisfy $x+y+z=(x-y)^{2}+(y-z)^{2}+(z-x)^{2}$

If $y^2-x^2\bigm|2^ky-1$ and $2^k-1\bigm|y-1$ then $y=2^k$ and $x=1$

Finding all natural $x$, $y$, $z$ satisfying $7^x+1=3^y+5^z$