BigInteger-friendly steppers added. MersenneResidueStepper converted to struct. Manual residue tracking replaced with steppers. Modulo operations replaced with steppers.

PerfectNumbers.Core/BigIntegerCycleRemainderStepper.cs

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+using System.Numerics;
+using System.Runtime.CompilerServices;
+
+namespace PerfectNumbers.Core;
+
+/// <summary>
+/// Maintains rolling remainders of an increasing sequence modulo a BigInteger cycle length.
+/// Mirrors <see cref="CycleRemainderStepper"/> for values that exceed 64 bits.
+/// </summary>
+[method: MethodImpl(MethodImplOptions.AggressiveInlining)]
+public struct BigIntegerCycleRemainderStepper(BigInteger cycleLength)
+{
+    private readonly BigInteger _cycleLength = cycleLength;
+    private BigInteger _previousValue = BigInteger.Zero;
+    private BigInteger _currentRemainder = BigInteger.Zero;
+
+	[MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public BigInteger Initialize(BigInteger value)
+    {
+        _previousValue = value;
+        _currentRemainder = value % _cycleLength;
+        return _currentRemainder;
+    }
+
+    [MethodImpl(MethodImplOptions.AggressiveInlining)]
+    public BigInteger ComputeNext(BigInteger value)
+    {
+        BigInteger delta = value - _previousValue;
+        _previousValue = value;
+        _currentRemainder += delta;
+        if (_currentRemainder >= _cycleLength)
+        {
+            _currentRemainder %= _cycleLength;
+        }
+
+        return _currentRemainder;
+    }
+}