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数论 MSE 4 票 2 回答 159 浏览 已读

Does $x_1^n + x_2^n + \dots + x_n^n = z^n$ have infinitely many primitive solutions in positive integers?

OHIH8
I am familiar with "Fermat's Last Theorem" and the disproved "Euler's sum of powers conjecture". By my understanding, the latter conjecture states that $n$ terms are required to have solutions, which has been disproved by counterexample. My question is whether or not you can always find an...
数论 MSE 1 票 1 回答 59 浏览 已读

Infinitude and asymptotic growth of a sparse recursively generated prime sequence

Nothing
Construction of the set: Start with an empty set F.Test primes in sequential order.A prime P is called "foundational" and belongs to F if and only if it is NOT representable as $$x_1 q_1^{a_1}+x_2 q_2^{a_2}+...+x_n q_n^{a_n}$$ Where ${q_1 ,q_2, q_3,...,q_n}$ are earlier primes of the set F and...
数论 MSE 1 票 1 回答 38 浏览 未读

Minimum value of $i$ to change $\lfloor n / i \rfloor$

insipidintegrator
I was solving this CSES question called Sum of Divisors and one of the solutions in the USACO Guide hints at this statement: The minimum value of $j > i$ such that $\lfloor n/j \rfloor$ < $\lfloor n/i \rfloor$ is $j = \lfloor n/q \rfloor + 1$, where $q = \lfloor n/i \rfloor$ for integers $j, i...