1your one post was enough to make it "tooo obvious" [3]
n1 and n2 are two numbers which on multiplying with 7 gives a number consisting only five's no number between n1 and n2 exists which on multiplying with 7 gives the same result.
Find n1 - n2
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18 Answers
1you dont really need conguencies to solve this one though it can be handy if you know
11HEy, where did congruence come from? We aren't talking about triangles.
341I used ≡, not =. Look up congruences. Loosely speaking, the remainder is 3 upon division by 7. But here remainder need not lie between 0 and 6
34155555..555(n times) = 5(1+10+102+...+10n-1)
Now 10≡3 mod 7,
So (1+10+102+...+10n-1) ≡ 1+3+32+...+3n-1 mod 7
checking for n=1,2,3 we get for n = 6, 1+3+3222+..+35 =364 ≡ 0 mod 7
Hence the number 555555 is the first such number.
Its obvious that the next such number can only be 555...555 (12 5s)
1since n1 and n2 are not necessarily the first such nos the general ans would be
79365 x 106k where k={1,2,3,4......}
hope i am not blabbering [4]