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### Questions (8)

 8 Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$ 4 Combinatorial proof for $\binom{n}{a}\binom{a}{k}\binom{n-a}{b-k} = \binom{n}{b}\binom{b}{k}\binom{n-b}{a-k}$? 4 $16$ natural numbers from $0$ to $9$, and square numbers: how to use the pigeonhole principle? 2 How many ordered pairs of positive integers 2 Combinatorial proof help

### Reputation (132)

 +10 Combinatorial proof for $\binom{n}{a}\binom{a}{k}\binom{n-a}{b-k} = \binom{n}{b}\binom{b}{k}\binom{n-b}{a-k}$? +5 $16$ natural numbers from $0$ to $9$, and square numbers: how to use the pigeonhole principle? +40 Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$ +5 How many ordered pairs of positive integers

### Tags (10)

 1 soft-question 0 integer-lattices 0 combinatorics × 5 0 number-theory 0 prime-numbers × 2 0 pigeonhole-principle 0 binomial-coefficients × 2 0 combinatorial-game-theory 0 elementary-number-theory × 2 0 permutations

### Account (1)

 Mathematics 132 rep 9