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@ @@Hßìÿa@ö§aI@†a‡Èÿa@óî‹Åä@

                                                    yx                ()

                                                       x +y
                                                       30 36

.   1   (  )            1   (  )             1   (  )   1     ()
   180                  90                   36         30

                  lcm (a,a + 2)                        a              ()

a(a + 2) ( )      a(a + 2) ( )               1( ) a + 2( )

    2

                  gcd(m , c ) m |b           gcd(b , c ) = 1          ()

   1( )                    b( )              m( )             c ()

                                                       n ()

   n 2 = 3k +1    n 2 = 3k ( )                      n 2 = 3k + 2 ( )
    n 2 = 4k +1    n2 = 4k ( )
                                                 n 2 = 4k + 2 ( )

                                                 [AHSME 1951]( )

                            n                          n3 −n

   6( )                 4( )                 3( )             2 ()

   abcabc                                        [AHSME 1951] (       )

   101 ( )    1001 ( )         13 11 ( )               11 7 ( )

1417 1059                                        [AHSME 1976] ( )

            d −r        r           d                  2312

   23 ( )               19 ( )      17 ( )              15 ( )

   ٢٥
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