Feat: Fermat factorization algorithm created.

.gitignore

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+.vscode/
+
+bin/
+
+obj/
+
+*.out
+
+*.o

Makefile

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+# cc and flags
+CC = g++
+CXXFLAGS = -std=c++11 -g -Wall
+LDFLAGS = -lgmp -lgmpxx
+#CXXFLAGS = -std=c++11 -O3 -Wall
+
+# folders
+INCLUDE_FOLDER = ./include/
+BIN_FOLDER = ./bin/
+OBJ_FOLDER = ./obj/
+SRC_FOLDER = ./src/
+
+# all sources, objs, and header files
+MAIN = Main
+TARGET = a.out
+SRC = $(wildcard $(SRC_FOLDER)*.cpp)
+OBJ = $(patsubst $(SRC_FOLDER)%.cpp, $(OBJ_FOLDER)%.o, $(SRC))
+
+$(shell mkdir -p $(OBJ_FOLDER))
+
+$(shell mkdir -p $(BIN_FOLDER))
+
+$(OBJ_FOLDER)%.o: $(SRC_FOLDER)%.cpp
+	$(CC) $(CXXFLAGS) -c $< -o $@ -I$(INCLUDE_FOLDER)
+
+all: $(OBJ)
+	$(CC) $(CXXFLAGS) -o $(BIN_FOLDER)$(TARGET) $(OBJ) ${LDFLAGS}
+
+clean:
+	@rm -rf $(OBJ_FOLDER)* $(BIN_FOLDER)*

include/fermat_factorization.hpp

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+#ifndef FERMAT_FACTORIZATION
+#define FERMAT_FACTORIZATION
+
+#include <gmpxx.h>
+
+mpz_class fermat_factorization(mpz_class n);
+
+#endif

src/fermat_factorization.cpp

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+#include "fermat_factorization.hpp"
+#include <cmath>
+
+mpz_class fermat_factorization(mpz_class n) {
+
+    mpz_class x = std::sqrt(n);
+
+    if (x*x == n) return x;
+
+
+    x++; mpz_class y2 = x*x - n;
+    mpz_class y = std::sqrt(y2);
+
+    while (y2 != y*y)
+    {
+        y2 += 2*x + 1; x++; 
+        y = std::sqrt(y2);
+    }
+
+    return x + y;
+}

src/main.cpp

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+#include <iostream>
+#include "fermat_factorization.hpp"
+
+int main()
+{
+    mpz_class n; std::cin >> n;
+    std::cout << fermat_factorization(n) << '\n';
+}