How many distinct postitive integers satisfy the identity $x+y+z+w = 100$?
3767
Constrained stars and bars.
4194
Which integers can be expressed as a sum of squares of two coprime integers?
149686
Combinatorics and trigonometry identity
58418
Does there exist a set of exactly five positive integers such that the sum of any three distinct elements is prime?
118036
Proving at least 99 pairwise sums of the reals are non-negative
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$
20713
The sum of an uncountable number of positive numbers
27141
Combinatorics identity question
62036
Finding the number of non-negative integral solutions of $x + y + z = 10$
83496
Math contest integer triplet problem: $x + y + z + xy + yz + xz = xyz − 1$
67899
Integer squares of the form $x^4+x^3+x^2+x+1$
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
137010
What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
56985
Show that every positive integer has a unique representation in the form $50k+l$...?
152167
Prove that if $x,y,z$ are integers such that $x^2+y^2=z^2$, then $xyz \equiv o \pmod{60}$.
65983
Combinatorial proof of binomial coefficient summation identity