Aug 25, 2022 · The goal of this question is to find if other methods exist to generate arbitrarily long sequences of consecutive numbers without primes. I started searching for other formulas …

May 16, 2016 · The sum of $a$ consecutive odd numbers is a difference of squares $ (n + a)^2 - n^2 = a (a + 2n)$.

Jun 6, 2017 · In terms of this structure, the composite topologies representing the composite region in the k-tuple ensure that the frontier prime elements are consecutive in the sequence …

Mar 6, 2023 · There is a problem asking me to prove the product of 3 consecutive integers is always divisible by 6 by using induction and not using the fact that one of the 3 numbers must …

Basically, on average, how many times one should roll to expect two consecutive sixes?

Jan 12, 2021 · @Baropryl In both of your examples, you construct your consecutive numbers such that the smaller of the two is the even number. You must explicitly consider the case that …

Feb 5, 2020 · There's a very simple proof. Consecutive numbers have different parities, and squaring preserves parity. The difference of numbers with different parities is odd.

Jan 12, 2015 · Sum of consecutive numbers Ask Question Asked 10 years, 10 months ago Modified 2 years, 8 months ago

Nov 25, 2025 · Minimum size of a sequence summing to $2013$ that guarantees a consecutive subset sum of $31$ (still wanted rigorous proof) Ask Question Asked 11 days ago Modified 9 …

Since they are consecutive, one is even and the other is odd. Now, squaring the even number is multiplying it an even number of times, so the answer is even. Squaring the odd number, …