n Let be a non-negative integer and suppose a = an · 10 +· ··+ aj •·10+ ao a = 0 Prove that mod 7 iff (a, · 10"-1 +...+ a2 · 10 + a1)–2ao = 0 mod 7. Use this result to devise an algorithm for determining whether an integer is divisible by 7.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.8: Adding And Subtracting Radicals
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n
Let
be a non-negative integer and suppose
a = an · 10" + · · ·+ a1 ·10 + ao
..
a = 0
Prove that
mod 7 iff
(an · 10"-1
+..+ a2 · 10+a1)–2ao = 0
mod
7. Use this result to devise an algorithm for
determining whether an integer is divisible by 7.
Transcribed Image Text:n Let be a non-negative integer and suppose a = an · 10" + · · ·+ a1 ·10 + ao .. a = 0 Prove that mod 7 iff (an · 10"-1 +..+ a2 · 10+a1)–2ao = 0 mod 7. Use this result to devise an algorithm for determining whether an integer is divisible by 7.
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