For each pair of numbers find integers 𝑥 and 𝑦 such that 𝑎𝑥 + 𝑏𝑦 =gcd (𝑎,𝑏)
a) 𝑎= 91, 𝑏=10
For the pair 𝑎=91,𝑏=10𝑎= 91, 𝑏=10a=91,b=10 of numbers let us find integers xxx and yyy such that 𝑎𝑥+𝑏𝑦=gcd(𝑎,𝑏).𝑎𝑥 + 𝑏𝑦 =gcd (𝑎,𝑏).ax+by=gcd(a,b).
Taking into account that 91=10⋅9+191=10\cdot9+191=10⋅9+1 and 10=10⋅1+0,10=10\cdot 1+0,10=10⋅1+0, we conclude that gcd(91,10)=1=91−10⋅9=91⋅1+10⋅(−9).gcd (91,10)=1=91-10\cdot 9=91\cdot 1+10\cdot(-9).gcd(91,10)=1=91−10⋅9=91⋅1+10⋅(−9). Consequently, x=1, y=−9.x=1,\ y=-9.x=1, y=−9.
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