\(A=p^2+59=a^xb^yc^z...\)(a khac b khac c...)
So Uoc cua A la: (x+1)(y+1)(z+1)...=6 =2.3.1...
=> x+1=2; y+1=3 => x=1;y=2
=>A =a.b2 voi a;b la SNT
+ Neu p =2 => A=63=a.b2 => a =7 ; b =3 (TM)
+Neu p =3 => p la so le => A=p2 + 59 =68 = 17.22
=> a =17 hoac b =2
+ Neu p>3 => p =3k+1 hoac p =3k +2
Ta lai co p2 +59 la so chan => a =2 hoac b =2
*Neu p = 3k+1 => A= (3k+1)2 +59 = a.b2 => 9k2 +6k+60=a.b2 chia het cho 3 => a=2 ; b =3 hoac a =3 ; b =2
=> A =p2 +59=2.32 =18 loai
A= p2 +59=3.22 =12 loai
*Neu p = 3k+2 => A= (3k+2)2 +59 = a.b2 => 9k2 +12k+63=a.b2 chia het cho 3 tuong tu tren
Vay p =2 hoac 3
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