MHB What Is (x+y) Mod 11 If A=52x1y3 Equals 4 Mod 11?

  • Thread starter Thread starter Albert1
  • Start date Start date
Albert1
Messages
1,221
Reaction score
0
$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?
 
Mathematics news on Phys.org
Albert said:
$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?
Hello.

If \ A \equiv{4 } \mod(11)

and

520103 \equiv{1 } \mod(11)

then

520183 \equiv{4 } \mod (11), \ for \ 80 \equiv{ 3} \mod(11)

Since:

1000 \equiv{10 } \mod(11)

and

10 \equiv{10 } \mod(11)

To increase it x in 1000 units is equivalent to diminish and in 10 units.

Therefore:

(x+y)=8

Regards.
 
Albert said:
$A=52x1y3$ is a 6 digits number
if $A$ mod 11=4
find $(x+y)$ mod 11=?

A mod 11 =-(5+x+y) + (2+1+3) mod 11 = 4

so (x+y-1) mod 11 = - 4

(x+y) mod 11 = -3 or 8 to make it positive
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Back
Top