Mixing
Largest number which leaves equal remainder with 3 given numbers
0
$begingroup$
N be the largest number that will divide 1315, 4675 and 6915, leaving the same remainder in each case. What is the
remainder?
number-theory
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
$endgroup$
add a comment |
0
$begingroup$
N be the largest number that will divide 1315, 4675 and 6915, leaving the same remainder in each case. What is the
remainder?
number-theory
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
$endgroup$
1
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04
add a comment |
0
0
0
$begingroup$
N be the largest number that will divide 1315, 4675 and 6915, leaving the same remainder in each case. What is the
remainder?
number-theory
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
$endgroup$
N be the largest number that will divide 1315, 4675 and 6915, leaving the same remainder in each case. What is the
remainder?
number-theory
number-theory
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
asked Jan 23 at 16:12
Devanshu SinglaDevanshu Singla
6
6
1
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04
add a comment |
1
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04
1
1
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04
add a comment |
0
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1
$begingroup$
Hint: $N$ divides the differences of each two so also the gcd of these differences (and the gcd $= 1120$ already works, so it is the largest such $N) $
$endgroup$
– Bill Dubuque
Jan 23 at 16:20
$begingroup$
But can we say that the value of N that we get is the largest?
$endgroup$
– Devanshu Singla
Jan 23 at 16:35
$begingroup$
$N$ divides the gcd, so $N$ can't be larger than the gcd.
$endgroup$
– Bill Dubuque
Jan 23 at 16:43
$begingroup$
"will divide" is an unlucky formulation when we can have a remainder. You mean, when those numbers are divided by $N$ , the remainder will be the same, right ?
$endgroup$
– Peter
Jan 26 at 14:04