(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E) where {s, t} € E if and only if 7 | (s – t) or 7| (s+t).
(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E) where {s, t} € E if and only if 7 | (s – t) or 7| (s+t).
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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Solve B
![(a) For all x, y = Z, prove that x¹y - x²y³ is even.
(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E)
where {s, t} € E if and only if 7 | (st) or 7| (s+t).
(c) Prove that in any set of four integers, there exists a pair x, y
such that 14 | (x4y - x²y³).
[Hint: Factor the expression. Consider integers modulo n, which
n would be relevant? What information can be gathered from
the connected components of the above graph?]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91bac8a8-89be-4b91-973b-d6b3f806c13e%2F71267d30-b3d1-481b-b82c-6ffa391fee5a%2Frqtxhak_processed.png&w=3840&q=75)
Transcribed Image Text:(a) For all x, y = Z, prove that x¹y - x²y³ is even.
(b) Let V = {0, 1, 2, 3,..., 13}. Draw the graph G = (V, E)
where {s, t} € E if and only if 7 | (st) or 7| (s+t).
(c) Prove that in any set of four integers, there exists a pair x, y
such that 14 | (x4y - x²y³).
[Hint: Factor the expression. Consider integers modulo n, which
n would be relevant? What information can be gathered from
the connected components of the above graph?]
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