document.write( "Question 1093280: Find the least residue of 5^8 (mod 7).
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Algebra.Com's Answer #707912 by rothauserc(4718) $\"\"$ $\"About$

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modulus example defining residue
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\n" ); document.write( "Given
\n" ); document.write( "a, there is only one value b between 0 and n−1 so that
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\n" ); document.write( "a ≡ b(mod n). We call b the residue of a modulo n, and write b = (a mod n).
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\n" ); document.write( "Note The expression a ≡ b(mod n) means that a-b is a multiple of n
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\n" ); document.write( "We are asked for the least residue of 5^8 (mod 7)
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\n" ); document.write( "5^8 / 7 = 390625 / 7 = 390621 with remainder of 4
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\n" ); document.write( "least residue of 5^8 (mod 7) is 4
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\n" ); document.write( "Note 11 ≡ 4(mod 7) as well
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