Use Problem 87 to solve each of these three simultaneous congruences. (a) x = 2 (mod 7), x = 5(mod 11), x = 11 (mod 17) (b) x = 0 (mod 7), x = 8(mod 11), x = 10 (mod 17) (c) x = 5 (mod 7), x = 6 (mod 11), x = 14 (mod 17)
Use Problem 87 to solve each of these three simultaneous congruences. (a) x = 2 (mod 7), x = 5(mod 11), x = 11 (mod 17) (b) x = 0 (mod 7), x = 8(mod 11), x = 10 (mod 17) (c) x = 5 (mod 7), x = 6 (mod 11), x = 14 (mod 17)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Q87 to slove Q90(c)
Transcribed Image Text:90. Use Problem 87 to solve each of these three simultaneous congruences.
(а) х —
2 (mod 7), x = 5 (mod 11), x = 11 (mod 17)
(b) x = 0 (mod 7), x = 8 (mod 11), x = 10 (mod 17)
(c) x = 5 (mod 7), x = 6 (mod 11), x = 14(mod 17)
Transcribed Image Text:87. Let M
тiт2 ... тп, where gcd(mi, my)
1 whenever i + j, and let
Mi
M/m;. Let y = b; (mod m;) be a solution to My = 1 (mod m;). Prove
that the simultaneous congruences
(mod m1)
(mod m2)
a2
(mod mn)
have the solution
x = a1b1 M1 + azbąM2 + azb3M3+……
+ anbn Mn (mod M).
III ||
II
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