How many natural numbers are there between 1000 and 2000, which when divided by 341 leaves remainder 5?
3
Step 1 — Form of the number: Any such number is \(N=341k+5\).
Step 2 — Apply the range \(1000<N<2000\):
\[995<341k<1995 \implies 2.92<k<5.85\]
Step 3 — Integer values: \(k=3,4,5\) give \(N=1028,1369,1710\).
Therefore there are 3 such numbers.
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