Page 84 - Numbertheory

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78 ( ) 60 ( ) 45 ( ) 33 ( )

nm [AHSME 1960] ( )
)
m2 −n2 . n<m )
)
8() 6( ) 4( ) 2() )

6( )

0,1, 3, 4 ( ) 0,1, 3 ( ) 0, 2 ( ) 0,1 ( )

1000 [ASMHE 1966] (

: 75

658 ( ) 684 ( ) 686 ( ) 688 ( )

10 12 −b a + 2 (

: a +b

7 ( ) 10 ( ) 5( ) 2 ()

(

2 12113 −1014 ()

178212 +184112 = 192212 ( )

3 3262 − 3252 ()

24 65314638792 ()

P [AHSME 1968] (

P.

3() 5( ) 6 ( ) 15 ( )

٧١