query: Idea of the Proof : Existence of a & b so that (Any integer greater than 8) = 3a + 5b
positive_passages.docid: 11359
positive_passages.text: Determine the Set of a Sum of Numbers
negative_passages.docid: 94209
negative_passages.text: Prove by contradiction that every integer greater than 11 is a sum of two composite numbers
negative_passages.docid: 91786
negative_passages.text: Proving and disproving $\exists b,c\in \mathbb R$ such that $f(x)=\frac a2x^2+bx+c $
negative_passages.docid: 1383
negative_passages.text: How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
negative_passages.docid: 33786
negative_passages.text: Proof that a certain fraction is always an integer
negative_passages.docid: 114780
negative_passages.text: $\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
negative_passages.docid: 101708
negative_passages.text: Integers can be expressed as $a^3+b^3+c^3-3abc$
negative_passages.docid: 65742
negative_passages.text: Strong Induction: Every natural number $n\geq 8$ can be represented as $n=3k + 5\ell$
negative_passages.docid: 126889
negative_passages.text: Proof by induction: inequality $n! > n^3$ for $n > 5$
negative_passages.docid: 140167
negative_passages.text: Proving $A+A'B=A+B$ without truth tables
negative_passages.docid: 20346
negative_passages.text: 'Algebraic' way to prove the boolean identity $a + \overline{a}*b = a + b$
negative_passages.docid: 24856
negative_passages.text: Proving sup(A + B) = sup A + sup B
negative_passages.docid: 101159
negative_passages.text: Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
negative_passages.docid: 146439
negative_passages.text: Is every sufficiently large positive integer of the form $ab + ac + bc + 1$?
negative_passages.docid: 46286
negative_passages.text: Prove if $a\mid b$ and $b\mid a$, then $|a|=|b|$ , $a, b$ are integers.
negative_passages.docid: 23141
negative_passages.text: How to prove that from "Every infinite cardinal satisfies $a^2=a$" we can prove that $b+c=bc$ for any two infinite cardinals $b,c$?
negative_passages.docid: 55673
negative_passages.text: Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?