Find the smallest positive integer solution to the following system of congruences: x -= 17(mod35) x -= 8(mod43)

Albarellak 2021-01-31 Answered
Find the smallest positive integer solution to the following system of congruences:
x17(mod35)
x8(mod43)
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Expert Answer

lamusesamuset
Answered 2021-02-01 Author has 93 answers
Given,
x17(mod35)
and
x8(mod43)
Step 2
Now x = 17 + 35k, for some kZ
Then,
17+35k8(mod43)
35k9(mod43)
35k34(mod43)
gcd(35,43)=1
Then, there exists x,yZ such that 35x + 43y = 1
35=4×8+3
43=35×1+8
8=3×2+2
Step 3
3=2×1+1
1=32×1
1=3(83×2)×1
1=3×38×1
1=3×(354×8)8×1
1=3×358×13
1=3×35(4335×1)×13
1=16×3543×13
1=35(16)+43(13)
Hence, x = 16
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