Directly 55591

If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5.
Prove directly

Correct answer:

x =  1

Step-by-step explanation:

nN n = 5 k1 +2  5 k2 +3  n2 = 5 k3+4 k1,k2,k3N  (5 k1 +2)2 = 25 k12 + 20 k1+4 = 5 (5 k11+4 k1)+4 = 5 k31+4 k31 = 5 k11+4 k1 (5 k2 +3)2 = 25 k22 + 30 k2+9 = 25 k22 + 30 k2+5+4 =  5 (5 k22+6 k2+1)+4 = 5 k32+4 k32=  5 k22+6 k2+1  x=1



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