Problem 63 solved

063.hs

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+-- Problem 63
+-- 13 February 2004
+--
+-- The 5-digit number, 16807=7^5, is also a fifth power. Similarly, the 9-digit number, 134217728=8^9, is a ninth power.
+--
+-- How many n-digit positive integers exist which are also an nth power?
+
+powers n = map (^n) [1..100]
+
+is_solution n x = (x >= 10^(n-1)) && (x < 10^n)
+
+find n = filter (is_solution n) (powers n)
+
+main = do
+    print $ sum $  map (length . find) [1..100]