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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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Transcribed Image Text:6. Let a be a number written in base 10 as
x = ao + a110 +..a, 10"
where 0< a; < 10.
(a) Prove that 2 divides a if and only if 2 divides ao.
(b) Prove that 4 divides a if and only if 4 divides ao +2a1.
(c) Prove that 8 divides a if and only if 8 divides ao + 2a1 + 4a2.
(d) Prove that 5 divides a if and only if 5 divides ao.
(e) Prove that 9 divides a if and only if 9 divides the sum ao + ...a, of its digits.
(f) Prove that 3 divides a if and only if 3 divides the sum ao + ...an of its digits.
(g) Prove that 11 divides a if and only if 11 divides the alternating sum ao – a1 + az
....
(h) Come up with a rule for dividing by 7 and prove that it works.
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