Question

AJUTORRRRRRRRRRRRRRRRRRRRRRRRRRRRRR!!! ​

Answer 1

abcd =nr par

abcd =patrat perfect

un p.p. nu poate acea ultima cifra para:  2 si 8.

=> d∈{4; 6}; d≠0; (un nr cu ultima cifra 0, poate fi p.p. daca si penultima cifra=0); dar cd≠0

ab: cd= 2 rest 19

=> ab=2•cd+19

abcd=ab•100+cd

=(2•cd+19)•100+cd

=200•cd+1900+cd

=201•cd+1900

=201(10c+d)+1900

abcd=2010•c+201•d+1900

d=4=> 2010c+201•4+1900=p.p.

2010c+2704=p.p.

c∈{1;2;3}; pentru c>3=> abcd>9999

c=1=> 2010+2704=4714≠p.p

c=2=>2•2010+2704=6724=82²

c=3=> 3•2010+2704=8734≠p.p.

d=6=> 2010c+201•6+1900=p.p.

2010c+3106=p.p.

c∈{1;2;3}; pentru c>3=> abcd>9999

c=1=> 2010+3106=5116≠p.p

c=2=>3•2010+3106=7126≠p.p

c=3=> 3•2010+3106=9136≠p.p.

abcd=6724=82²

67:24=2 rest 19