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Prove that $n^4 + 4^n$ is not a prime for all $n > 1$ and $n \in \mathbb {n}$ Having a tough time with this problem, i feel that brute force is a possibility. This question appeared in the undergrad entrance exam of the indian statistical institute.
What are the numbers that have at least four distinct prime factors up to $500$ Find all positive integers $n$ such that $n$,$n + 2$, and $n + 4$ are all primes The first number is $210$ and the four factors are($2,3,5,7$) next number is $330 \\ (2,3,5,11)$
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Is $545^4 + 4^ {545}$ a prime number I tried writing the expression as, $$545^4 + 4*4^ {544}$$ thus we get, $$545^4 +. Are primes equally likely to be equivalent to $1$ or $3$ modulo $4,$ or is there a skew in one direction That is my specific question, but i would be interested to know if there.
I am told to find the smallest number with 4 different prime factorizations in this world A number is prime if it. For any integer $n$ greater than $1$, show that $4^n+n^4$ is never a prime number I tried to use mathematical induction, but somehow could not manage to prove it.
A prime divisor of $m^2+1$ for an integer $m$ is either $2$ or equal to $1$ ($\bmod$ $4$)
Then your argument can be adapted a bit to show that a finite number of such. The number $n^4 + 4$ is never prime for $n>1$ ask question asked 11 years, 7 months ago modified 11 years ago Since n>1, i took the base case as n=2 and found that the given expression is equal to 49 which is certainly not a prime Hence, the proposition is true for n=2.
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