If R is the remainder when each of the numbers 1059, 1417, and 2312 is divided by D, where D is an integer greater than 1, compute the value of D - R.
Let p,q,r,s,t be some arbitrary integers, then
A=1059 = pD+R
B=1417 = qD+R
C=2312 = rD+R
E = B-A = sD = 358 = 2*179
F = C-B = tD = 895 = 5*179
Using Euclid's algorithm, all common factors between E and F are also common factors of (A-R),(B-R) and (C-R).
Thus 179 is the (only) common factor between the three numbers (A-R), (B-R) and (C-R), from which we determine that D=179 and R=164.
D-R=179-164=15.
1417-1059=358=2*179
2312-1417=895=5*179
D=179
R=164
D-R=15
To calculate the value of D - R, we need to find the remainder (R) when each of the given numbers is divided by D. Let's go step by step.
First, let's find the remainder (R) when 1059 is divided by D. We can use the modulo operator (%) to find the remainder.
R1 = 1059 % D
Next, let's find the remainder (R) when 1417 is divided by D.
R2 = 1417 % D
Finally, let's find the remainder (R) when 2312 is divided by D.
R3 = 2312 % D
Now that we have the remainders (R1, R2, R3), we can calculate the value of D - R by subtracting the remainder from D.
D - R = D - (R1 + R2 + R3)
However, without additional information or constraints on the values of R1, R2, and R3, we cannot determine the exact value of D - R or D.
You would need more information about the specific values of R1, R2, R3, or any relationships between the remainders to calculate the required value accurately.