Question

fie s(n) cifra nr natural n.determinati toate numerele naturale n pentru care n-s(n)=2007​

Answer 1

Fie n=abcd, numar de 4 cifre; abcd=1000a+100b+10c+d

suma cifrelor= s(n)= a+b+c+d

n-s(n)=1000a+100b+10c+d-(a+b+c+d)

999a+99b+9c=2007

9(111a+11b+c)=9•223

111a+11b+c=223

=> a=2 ; b=0; c=1; d∈{0,1,2,3,4....9}

abcd ∈{2010, 2011, 2012, 2013, ......, 2019}

n∈{2010, 2011, 2012, 2013, ......, 2019}