3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.
3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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![3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.
Hint: considering splitting into cases where integers are of the form a·k+b or (a.k+b)
for ke N where a and b are fixed for a given case, b varies over the cases and the least
significant digit of the integer depends on only b.
Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respec-
tively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59cc5c96-5b3d-4dc4-84c8-b0ec8fef76d5%2Ff1cfa0be-82f5-44c2-aac8-587232b77a41%2Fj6n1is_processed.png&w=3840&q=75)
Transcribed Image Text:3. Prove that least significant digit of the square of an even integer is either 0, 4, or 6.
Hint: considering splitting into cases where integers are of the form a·k+b or (a.k+b)
for ke N where a and b are fixed for a given case, b varies over the cases and the least
significant digit of the integer depends on only b.
Note: the least significant digit of an integer is the digit farthest to the right in a
integer. For example, the least significant digits of 1007 and 26 are 7 and 6 respec-
tively.
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