Răspuns :
p = ( 1 +2 ) ( 1+ 2² ) 1 +2⁴ ) ( 1 + 2⁸ ) ( 1 + 2¹⁶) ( 1 + 2³²)( 1 + 2⁶⁴)
inmultim ex. cu 1 - 2
p( 1 - 2 ) =[ (1 -2) ( 1 +2 )] ( 1+ 2² ) 1 +2⁴ ) ( 1 + 2⁸ ) ( 1 + 2¹⁶ ) ( 1 + 2³² )( 1 +2⁶⁴)
↓
= 1 - 2²
=[ ( 1 - 2² ) ( 1+ 2² ) ](1 +2⁴ ) ( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴)
↓
=[( 1 - 2⁴ ) 1 +2⁴ ) ]( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2⁸ ) ( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2¹⁶ ) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2³² ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2⁶⁴ ) ( 1 +2⁶⁴ ) =
= 1 - 2¹²⁸
p( -1 ) = 1 - 2¹²⁸
p = 2¹²⁸ - 1
inmultim ex. cu 1 - 2
p( 1 - 2 ) =[ (1 -2) ( 1 +2 )] ( 1+ 2² ) 1 +2⁴ ) ( 1 + 2⁸ ) ( 1 + 2¹⁶ ) ( 1 + 2³² )( 1 +2⁶⁴)
↓
= 1 - 2²
=[ ( 1 - 2² ) ( 1+ 2² ) ](1 +2⁴ ) ( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴)
↓
=[( 1 - 2⁴ ) 1 +2⁴ ) ]( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2⁸ ) ( 1 + 2⁸) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2¹⁶ ) ( 1 + 2¹⁶ ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2³² ) ( 1 + 2³² )(1 +2⁶⁴) =
↓
= ( 1 - 2⁶⁴ ) ( 1 +2⁶⁴ ) =
= 1 - 2¹²⁸
p( -1 ) = 1 - 2¹²⁸
p = 2¹²⁸ - 1