Using the Chinese Remainder Theorem Solve the following:Here is the theorem first:Chinese Remainder Theorem (CRT): Let r, m1, . . . , mr ∈ Z and for all 1 ≤ i ̸= j ≤ rsuppose gcd(mi, mj ) = 1. Then for any r integers a1, . . . , ar, the system of linearcongruencesx = a1 (mod m1)x = a2 (mod m2)...x = ar (mod mr)has a solution x ∈ Z and it is unique modulo m1m2 · · · mr, i.e. if y ∈ Z is any othersolution, then y = x (mod m1m2 · · · mr).Find the smallest integer a > 2 such that 2 | a, 3 | a + 1, 4 | a + 2,5 | a + 3, and 6 | a + 4

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Answered: Using the Chinese Remainder Theorem…

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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Using the Chinese Remainder Theorem Solve the following:

Here is the theorem first:

Chinese Remainder Theorem (CRT): Let r, m₁, . . . , mr ∈ Z and for all 1 ≤ i ̸= j ≤ r
suppose gcd(m_i, m_j ) = 1. Then for any r integers a₁, . . . , a_r, the system of linear
congruences
x = a₁ (mod m₁)
x = a₂ (mod m₂)
.
.
.
x = a_r (mod m_r)
has a solution x ∈ Z and it is unique modulo m₁m₂ · · · m_r, i.e. if y ∈ Z is any other
solution, then y = x (mod m₁m₂ · · · m_r).