D = 179, R = 164
so d-r = 179-164 = 15
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
6 answers
This is a very challenging question, and a very brilliant answer by Reiny.
I would attempt the problem the following way. Let me know if it is correct.
We are given three numbers with an unknown offset. The three (original) numbers have a common factor. We are to find the common factor and the unknown offset.
We can find the unknown common factor by Euclid's method, which is to take the difference of the three numbers in turn and find the HCF of the differences.
1417-1059=358
2312-1417=895
D=HCF(895,358)=179
Check:
1059/179=5 R 164
1417/179=7 R 164
2312/179=12 R 164
D-R=179-164=15 same answer as Reiny.
I would attempt the problem the following way. Let me know if it is correct.
We are given three numbers with an unknown offset. The three (original) numbers have a common factor. We are to find the common factor and the unknown offset.
We can find the unknown common factor by Euclid's method, which is to take the difference of the three numbers in turn and find the HCF of the differences.
1417-1059=358
2312-1417=895
D=HCF(895,358)=179
Check:
1059/179=5 R 164
1417/179=7 R 164
2312/179=12 R 164
D-R=179-164=15 same answer as Reiny.
15
It is possible to use a guess and check method to acquire this result. Not typically associated with math past algebra 1, but a very useful method in finding a result.
Why to not su tract 2312 -1059
GDJF
=15
=15
4 answers