Question #266114

For each pair of numbers find integers 𝑥 and 𝑦 such that 𝑎𝑥 + 𝑏𝑦 =gcd (𝑎,𝑏)


a) 𝑎= 91, 𝑏=10



1
Expert's answer
2021-11-15T18:32:35-0500

For the pair 𝑎=91,𝑏=10𝑎= 91, 𝑏=10 of numbers let us find integers xx and yy such that 𝑎𝑥+𝑏𝑦=gcd(𝑎,𝑏).𝑎𝑥 + 𝑏𝑦 =gcd (𝑎,𝑏).

Taking into account that 91=109+191=10\cdot9+1 and 10=101+0,10=10\cdot 1+0, we conclude that gcd(91,10)=1=91109=911+10(9).gcd (91,10)=1=91-10\cdot 9=91\cdot 1+10\cdot(-9). Consequently, x=1, y=9.x=1,\ y=-9.


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