query: Why every second even number have same number of even and odd Divisors.
positive_passages.docid: 151508
positive_passages.text: How to determine number with same amount of odd and even divisors
negative_passages.docid: 91044
negative_passages.text: Why is a number that is divisible by $2$ and $3$, also divisible by $6$?
negative_passages.docid: 11976
negative_passages.text: Help with a recurrence with even and odd terms
negative_passages.docid: 107105
negative_passages.text: Is an irrational number odd or even?
negative_passages.docid: 105837
negative_passages.text: XORing consecutive integers has an interesting property. Does anyone know why?
negative_passages.docid: 21383
negative_passages.text: Can every even integer be expressed as the difference of two primes?
negative_passages.docid: 85272
negative_passages.text: $3x + 1$ is even iff $5x-2$ is odd
negative_passages.docid: 107371
negative_passages.text: Why round to even integers?
negative_passages.docid: 62251
negative_passages.text: "Maximum common divisor" for entire functions
negative_passages.docid: 25332
negative_passages.text: Why are even/odd functions called even/odd?
negative_passages.docid: 123267
negative_passages.text: Proving that even numbers equal the sum of two odd numbers.
negative_passages.docid: 72511
negative_passages.text: If $n$ is an odd natural number, then $8$ divides $n^{2}-1$
negative_passages.docid: 57746
negative_passages.text: Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
negative_passages.docid: 79219
negative_passages.text: Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
negative_passages.docid: 127848
negative_passages.text: Determine which Fibonacci numbers are even
negative_passages.docid: 129680
negative_passages.text: Prove that $n$ is even.
negative_passages.docid: 75229
negative_passages.text: Can there be a function that's even and odd at the same time?