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 Nov28 revised Trigonometry triangles expanded answer Nov24 revised Proving for every odd number $x$, $x^2$ is always congruent to $1$ or $9$ modulo $24$ typos Nov22 revised Limit of $\left(1-\frac{1}{n^2}\right)^n$ fixed missing minus signs Nov18 revised Prove that one of the numbers k,k+1, . . . ,k+(n-1) is divisible by n. Changed k to n assuming the problem is not as trivial as written Nov18 revised Proving $n^3$ is even iff $n$ is even add relationship to prime factorization theorem Mar21 revised Factorials and Arithmetic Progression. fix spelling and typos Jan29 revised bound for the product of numbers Fixed a missing factor of 2 Jan5 revised Inverting $\frac{\log(p-1)}{\log\ p}$ Update of further work and conclusion by the requestor. Dec29 revised How can I prove this inequality involving the primes? Found a typo Dec27 revised Unique digit fraction Noted inconsistency in problem statement. Dec27 revised faster and unconventional way of doing maths problem? Fixing missing text from problem