Answer to Question #178142 in Combinatorics | Number Theory for Khan

Question #178142

Find the integer a such that a ≡ 08(mod23) and −22 ≤ a ≤ 0. 


1
Expert's answer
2021-04-15T06:57:19-0400

The congruence relation may be rewritten as


"a=23k+8, where \\space k-integer"

if


"-22\\leq a \\leq 0"

then


"-22\\leq 23k+8 \\leq 0""-30\\leq 23k \\leq -8"

so

"k=-1"

and


"a=23k+8=23(-1)+8=-15""-15\\equiv8(mod 23)\\space and \\space -22\\leq -15 \\leq 0"

Answer: a=-15


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