diff --git a/CHANGELOG.md b/CHANGELOG.md
index ecedd437fc..6eaba53c6d 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -90,6 +90,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed a bug where negative or oversized segment sizes were not rejected in binary matching
 - Fixed the `network` mdns configuration to read the documented `host` key; the previously
   required, undocumented `hostname` key is still accepted
+- Fixed `rem` returning wrong results on 32-bit builds when an operand is a big integer with
+  a 64-bit magnitude, such as `(1 bsl 63) rem 7`
 
 ## [0.7.0-alpha.1] - 2026-04-06
 
diff --git a/src/libAtomVM/bif.c b/src/libAtomVM/bif.c
index 42cae38ee8..20849bcaeb 100644
--- a/src/libAtomVM/bif.c
+++ b/src/libAtomVM/bif.c
@@ -1443,7 +1443,7 @@ static term rem_boxed_helper(Context *ctx, uint32_t fail_label, uint32_t live, t
         RAISE_ERROR_BIF(fail_label, BADARITH_ATOM);
     }
     if (term_is_boxed_integer(arg2)) {
-        size |= term_boxed_size(arg2);
+        size = MAX(size, (int) term_boxed_size(arg2));
     } else if (UNLIKELY(!term_is_integer(arg2))) {
         TRACE("error: arg1: 0x%lx, arg2: 0x%lx\n", arg1, arg2);
         RAISE_ERROR_BIF(fail_label, BADARITH_ATOM);
@@ -1466,8 +1466,7 @@ static term rem_boxed_helper(Context *ctx, uint32_t fail_label, uint32_t live, t
         }
 
 #if BOXED_TERMS_REQUIRED_FOR_INT64 == 2
-        case 2:
-        case 3: {
+        case 2: {
             avm_int64_t val1 = term_maybe_unbox_int64(arg1);
             avm_int64_t val2 = term_maybe_unbox_int64(arg2);
             if (UNLIKELY(val2 == 0)) {
diff --git a/tests/erlang_tests/bigint.erl b/tests/erlang_tests/bigint.erl
index 2a5ab2fba4..431028563b 100644
--- a/tests/erlang_tests/bigint.erl
+++ b/tests/erlang_tests/bigint.erl
@@ -259,8 +259,27 @@ test_rem() ->
     ),
     <<"E3AE0EA63AE33EA79B071316BC9A7F1B">> = erlang:integer_to_binary(Int8 rem Int9, 16),
 
+    % operands with a 64-bit magnitude take 3 boxed terms on 32-bit builds and
+    % must not be mistaken for regular 2-term boxed int64 values
+    Int10 = erlang:binary_to_integer(?MODULE:id(<<"8000000000000000">>), 16),
+    Int11 = erlang:binary_to_integer(?MODULE:id(<<"8000000000000005">>), 16),
+    Int12 = erlang:binary_to_integer(?MODULE:id(<<"-8000000000000001">>), 16),
+    Int13 = erlang:binary_to_integer(?MODULE:id(<<"FFFFFFFFFFFFFFFF">>), 16),
+    Int14 = erlang:binary_to_integer(?MODULE:id(<<"7FFFFFFFFFFFFFFF">>), 16),
+
+    1 = Int10 rem ?MODULE:id(7),
+    808 = Int10 rem ?MODULE:id(1000),
+    8 = Int10 rem ?MODULE:id(1073741825),
+    -2 = Int12 rem ?MODULE:id(7),
+    5 = ?MODULE:id(5) rem Int13,
+    5 = Int13 rem ?MODULE:id(10),
+    42 = ?MODULE:id(42) rem Int10,
+    <<"7FFFFFFFFFFFFFFF">> = erlang:integer_to_binary(Int14 rem Int11, 16),
+    <<"8000000000000000">> = erlang:integer_to_binary(Int10 rem Int11, 16),
+
     ok = expect_error(badarith, fun() -> Int0 rem ?MODULE:id(0) end),
     ok = expect_error(badarith, fun() -> Int1 rem ?MODULE:id(0) end),
+    ok = expect_error(badarith, fun() -> Int10 rem ?MODULE:id(0) end),
 
     0.