Modular incongruences and Chinese Remainder Theorem
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Is there a way to adapt the Chinese remainder theorem to solve a series of modular incongruences, e.g.
$n notequiv 0 (textrm{mod } 5)$
$n notequiv 0 (textrm{mod } 6)$
$n notequiv 0 (textrm{mod } 7)$
(I know there are ways to solve this without modular arithmetic or CRT; looking for ways that do involve them)
number-theory modular-arithmetic chinese-remainder-theorem
asked Nov 13 at 16:58
ubadub
1236
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up vote
0
down vote
favorite
Is there a way to adapt the Chinese remainder theorem to solve a series of modular incongruences, e.g.
$n notequiv 0 (textrm{mod } 5)$
$n notequiv 0 (textrm{mod } 6)$
$n notequiv 0 (textrm{mod } 7)$
(I know there are ways to solve this without modular arithmetic or CRT; looking for ways that do involve them)
number-theory modular-arithmetic chinese-remainder-theorem
asked Nov 13 at 16:58
ubadub
1236
See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Is there a way to adapt the Chinese remainder theorem to solve a series of modular incongruences, e.g.
$n notequiv 0 (textrm{mod } 5)$
$n notequiv 0 (textrm{mod } 6)$
$n notequiv 0 (textrm{mod } 7)$
(I know there are ways to solve this without modular arithmetic or CRT; looking for ways that do involve them)
number-theory modular-arithmetic chinese-remainder-theorem
asked Nov 13 at 16:58
ubadub
1236
Is there a way to adapt the Chinese remainder theorem to solve a series of modular incongruences, e.g.
$n notequiv 0 (textrm{mod } 5)$
$n notequiv 0 (textrm{mod } 6)$
$n notequiv 0 (textrm{mod } 7)$
(I know there are ways to solve this without modular arithmetic or CRT; looking for ways that do involve them)
number-theory modular-arithmetic chinese-remainder-theorem
number-theory modular-arithmetic chinese-remainder-theorem
asked Nov 13 at 16:58
ubadub
1236
asked Nov 13 at 16:58
ubadub
1236
asked Nov 13 at 16:58
ubadub
1236
asked Nov 13 at 16:58
ubadub
1236
asked Nov 13 at 16:58
ubadub
1236
1236
See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25
add a comment |
See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25
See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25
See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25
add a comment |
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See the links on sieving that I gave here
– Bill Dubuque
Nov 13 at 18:25