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How would I answer the following set of questions related to discrete mathematics?

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#discrete-mathematics #proof-writing #induction #gcd-and-lcm
76
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Show that if $a_1b_2 − a_2b_1 = \pm 1$, then the gcd of $(a_1 + a_2, b_1 + b_2) = 1$

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#elementary-number-theory #gcd-and-lcm
1k
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Proof of associativity of GCD?

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#number-theory #elementary-number-theory #proof-verification #gcd-and-lcm
567
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Description of the lattice that gcd and lcm form on a PID

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#abstract-algebra #gcd-and-lcm #principal-ideal-domains #least-common-multiple
105
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Proofs about divisibility that seem obvious but eludes me

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#elementary-number-theory #divisibility #gcd-and-lcm
272
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If $\gcd(a,b)=1$ prove that $(a^2,b^2)=1$ or $2$.

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#gcd-and-lcm
279
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Greatest odd divisor function problem

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#number-theory #gcd-and-lcm #geometric-progressions
282
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Prove $\gcd(ab, c)\le \gcd(a,c)\gcd(b,c)$

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#elementary-number-theory #gcd-and-lcm
145
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Solve $x+y=84, \; \operatorname{lcm}(x,y) = \big( \gcd(x,y) \big)^2$

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#elementary-number-theory #arithmetic #gcd-and-lcm #least-common-multiple
110
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Finding the complex roots of a polynomial f knowing that it shares one root with a polynomial g

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#polynomials #gcd-and-lcm #euclidean-algorithm
1.7k
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How to find gcd of $(a,a^n)$

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#elementary-number-theory #gcd-and-lcm #euclidean-algorithm
15
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Invalid solutions as common factors

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#gcd-and-lcm
235
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A woman paid a $\$9.75$ debt using only dimes and quarters. In how many ways is this possible?

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#elementary-number-theory #gcd-and-lcm #euclidean-algorithm
318
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How to prove $\gcd(a, b) = ax + by$

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#proof-writing #gcd-and-lcm
37
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How to prove the following statement: $\gcd(a,b) = 1$ and $a=bc$ implies $a\mid c$

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#elementary-number-theory #divisibility #gcd-and-lcm

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